# Devry MATH221 Full Course Latest 2019 JULY

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Subject: Mathematics
Due on: 08/22/2019
Posted On: 08/22/2019 05:49 AM
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MATH221 Statistics for Decision Making

Week 1 Discussion

DESCRIPTIVE STATISTICS

If you were given a large data set, such as the sales over the last year of our top 100 customers, what might you be able to do with these data? What might be the benefits of describing the data?

Alternative: Look for examples of descriptive statistics in the news or on websites. Then post a link to that publication or site, note the statistic used and determine if it was an appropriate use of that statistic.

MATH221 Statistics for Decision Making

Week 2 Discussion

PROBABILITIES IN REAL WORLD

Look online and find an article published within the past 4 weeks that includes a reference to probabilities, means, or standard deviations. These articles might be discussing weather events, investing outcomes, or sports performance, among many other possible topics.

Your first post should include a summary of the article and what numbers you are highlighting from that article. Also include a link to the actual article. In your replies to other students, describe specific decisions that the statistic might influence and whether a different statistic might be more appropriate.

MATH221 Statistics for Decision Making

Week 3 Discussion

DISCRETE PROBABILITY VARIABLES

For this discussion you will use technology to create a short 1-2 minute multimedia post/presentation.

Suggestions: Narrated PowerPoint, recorded video (.mp4), Screencast-O-Matic (.mp4), or a similar tool of your choice. Video can be recorded directly within a post as well, but make sure to plan out in advance what you are going to say/show. There should be a visual component as well as audio, so if you are using a webcam for the video that only shows you speaking, please attach your PowerPoint slide(s) (or screenshot images of them) to the post as well so everyone can see them.

In your short presentation, you will be describing an example that uses discrete probabilities or distributions. Provide an example that follows either the binomial probabilities or any discrete probability distribution, and explain why that example follows that distribution. In your responses to other students, make up numbers for the example provided by that other student, and ask a related probability question. Then show the work (or describe the technology steps) and solve that probability example.

For more information about Narrated PowerPoint, access the Student Resources section of Course Resources under the Introduction & Resources module heading, and look for the heading that corresponds to the tool you want to use. For all media posts in this course, please include a brief written synopsis to inform your classmates what the main point or purpose is that the linked, attached, or embedded media addresses.

MATH221 Statistics for Decision Making

Week 4 Discussion

INTERPRETING NORMAL DISTRIBUTIONS

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

MATH221 Statistics for Decision Making

Week 5 Discussion

CONFIDENCE INTERVAL CONCEPTS

Look in the newspapers, magazines, and other news sources for results of a survey or poll that show the confidence interval, usually shows as a +/- some amount. Describe the survey or poll and then describe the interval shown. How does knowing the interval, rather than just the main result, impact your view of the results?

MATH221 Statistics for Decision Making

Week 6 Discussion

HYPOTHESES IN THE REAL WORLD

Consider a business of any type. What is a situation where a hypothesis test might help make a decision? Describe the situation. Then you or someone in a reply can make up numbers for that situation and someone else can solve it.

MATH221 Statistics for Decision Making

Week 7 Discussion

REGRESSION

Suppose you are given data from a survey showing the IQ of each person interviewed and the IQ of his or her mother. That is all the information that you have. Your boss has asked you to put together a report showing the relationship between these two variables. What could you present and why?

MATH221 Statistics for Decision Making

Week 8 REFLECTION PAPER

The Reflection Paper is due this week. Please refer to the Reflection Paper Overview for a full description of this assignment

Note: This assignment uses TurnItIn. To review the TurnItIn results for your submitted paper, look for this assignment in the Gradebook and click the colored icon to open the TurnItIn Originality Report.

MATH221 Statistics for Decision Making

Week 1 Homework

Question 1 The age of every fourth person entering a department store. The selected individuals would be considered a:

Homework Help:

1DA. Population/parameter/sample/statistic/inferential/descriptive (Links to an external site.) (DOCX)

Parameter

Sample

Population

Statistic

Question 2 In a survey of 1000 adults, 34% found they prefer charcoal to gas grills. The 1000 would be considered a:

Homework Help:

1DA. Population/parameter/sample/statistic/inferential/descriptive (Links to an external site.) (DOCX)

Population

Sample

Statistic

Parameter

Question 3 The chances of winning the Maryland lottery are one chance in twenty-two million. The probability would be considered an example of:

Homework Help:

1DA. Population/parameter/sample/statistic/inferential/descriptive (Links to an external site.) (DOCX)

Experiment design

A sample

Inferential statistics

Descriptive statistics

Question 4 The ages of 20 first graders would be considered:

Homework Help:

1DB. Qualitative/quantitative/nominal/ordinal/interval/ratio (Links to an external site.) (DOCX)

Qualitative data

Interval data

Nominal data

Quantitative data

Question 5

Marriage status (married, single, etc.) of the faculty at a university would be considered:

Homework Help:

1DB. Qualitative/quantitative/nominal/ordinal/interval/ratio (Links to an external site.) (DOCX)

Qualitative data

Ordinal data

Quantitative data

Ratio data

MATH221 Statistics for Decision Making

Week 2 Homework

Question 1 According to company records, the probability that a washing machine will break in the first year is 4%. This would be considered:

Homework Help:

2DA. Definition of probabilities and classical, empirical, subjective probabilities (Links to an external site.) (DOCX)

Classical probability

Subjective probability

Manufactured probability

Empirical probability

Question 2 Given the following information, find the probability that a randomly selected student will be very short. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21

Homework Help:

2DB. Probabilities from a given distribution of frequencies (Links to an external site.) (DOCX)

21.0%

28.8%

21.6%

39.4%

Question 3 Given the following information, find the probability that a randomly selected dog will be a golden retriever or a poodle. Number of dogs who are poodles: 31, golden retrievers: 58, beagles: 20, pugs: 38

Homework Help:

2DB. Probabilities from a given distribution of frequencies (Links to an external site.) (DOCX)

60.5%

46.9%

39.5%

58.0%

Question 4 Given that there is a 22% chance it will rain on any day, what is the probability that it will rain on the first day and be clear (not rain) on the next two days?

Homework Help:

2VA: Probabilities given probability of success and 2 or more events (Links to an external site.) (0:51)

2DC. Probabilities given probability of success and 2 or more events (Links to an external site.) (DOCX)

13.4%

17.2%

1.1%

78.0%

Question 5 Consider the following table. What is the probability of red?

Red Blue Total

Yes 15 21 36

No 38 13 51

Total 53 34 87

Homework Help:

2VB: Conditional probabilities from a table (Links to an external site.) (1:45)

15/53

36/87

15/87

53/87

MATH221 Statistics for Decision Making

Week 3 Homework

Question 1Let x represent the number of pets in pet stores. This would be considered what type of variable:

Homework Help:

3DA. Discrete versus continuous variables (Links to an external site.) (DOCX)

Discrete

Nonsensical

Lagging

Continuous

Question 2Let x represent the height of corn in Oklahoma. This would be considered what type of variable:

Homework Help:

3DA. Discrete versus continuous variables (Links to an external site.) (DOCX)

Distributed

Discrete

Continuous

Inferential

Question 3Consider the following table.

Age Group Frequency

18-29 9831

30-39 7845

40-49 6869

50-59 6323

60-69 5410

70 and over 5279

If you created the probability distribution for these data, what would be the probability of 40-49?

Homework Help:

3DB. Probabilities from a probability distribution (Links to an external site.) (DOCX)

42.5%

23.7%

18.9%

16.5%

Question 4Consider the following table.

Weekly hours worked Probability

1-30 (average=23) 0.08

31-40 (average=36) 0.16

41-50 (average=43) 0.72

51 and over (average=54) 0.04

Find the mean of this variable.

Homework Help:

3VA. Calculating the mean, variance, and standard deviation of discrete variables (Links to an external site.) (4:35)

3DC. Mean, expected value, variance, and standard deviation of discrete variables (Links to an external site.) (DOCX)

39.0

40.7

39.5

40.0

Question 5Consider the following table.

Defects in batch Probability

0 0.09

1 0.24

2 0.41

3 0.12

4 0.10

5 0.04

Find the variance of this variable.

Homework Help:

3VA. Calculating the mean, variance, and standard deviation of discrete variables (Links to an external site.) (4:35)

3DC. Mean, expected value, variance, and standard deviation of discrete variables (Links to an external site.) (DOCX)

1.48

1.43

1.22

2.02

MATH221 Statistics for Decision Making

Week 4 Homework

Question 1 The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase. Is this outcome unusual?

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.) (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.) (DOCX)

Probability is 0.03, which is usual as it is not less than 5%

Probability is 0.97, which is unusual as it is greater than 5%

Probability is 0.03, which is unusual as it is less than 5%

Probability is 0.97, which is usual as it is greater than 5%

Question 2 Monthly water bills for a city have a mean of \$108.43 and a standard deviation of \$36.98. Find the probability that a randomly selected bill will have an amount greater than \$173, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.) (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.)(DOCX)

Probability is 0.04, which is unusual as it is not less than 5%

Probability is 0.04, which is usual as it is less than 5%

Probability is 0.04, which is unusual as it is less than 5%

Probability is 0.04, which is usual as it is not less than 5%

Question 3 In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill.

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.) (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.)(DOCX)

0.70

Less than 1%

0.40

0.30

Question 4 A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.98mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.50mm. Would this outcome warrant a refund (meaning that it would be unusual)?

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.) (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.)(DOCX)

Probability of 0.09 and would not warrant a refund

Probability of 0.09 and would warrant a refund

Probability of 0.91 and would warrant a refund

Probability of 0.91 and would not warrant a refund

Question 5 A grocery stores studies how long it takes customers to get through the speed check lane. They assume that if it takes more than 10 minutes, the customer will be upset. Find the probability that a randomly selected customer takes more than 10 minutes if the average is 7.45 minutes with a standard deviation of 1.04 minutes.

Homework Help:

4VA. Calculating normal probabilities (Links to an external site.) (2:18)

4DA. Description of normal distribution, area, and probabilities, definition of unusual events (Links to an external site.)(DOCX)

0.007

0.501

0.993

0.071

MATH221 Statistics for Decision Making

Week 5 Homework

Question 1 From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 21.69 with a population standard deviation of 3.23. What is the 95% confidence interval for the amount of time spent on administrative issues?

Homework Help:

5VA. Calculating confidence intervals (Links to an external site.) (4:04)

5DA. Concept and meaning of confidence intervals (Links to an external site.) (DOCX)

(21.78, 22.60)

(19.24, 24.14)

(20.71, 22.67)

(20.86, 22.52)

Question 2 If a confidence interval is given from 43.83 up to 61.97 and the mean is known to be 52.90, what is the margin of error?

Homework Help:

5DB. Finding margin of error from given confidence interval (Links to an external site.) (DOCX)

43.83

18.14

4.54

9.07

Question 3 If a car manufacturer wanted lug nuts that fit nearly all the time, what characteristics would be better?

Homework Help:

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)

narrow confidence interval at low confidence level

wide confidence interval with high confidence level

wide confidence interval with low confidence level

narrow confidence interval at high confidence level

Question 4 Which of the following are most likely to lead to a narrow confidence interval?

Homework Help:

5DD. Changes in confidence interval based on changes in standard deviation or sample size (Links to an external site.) (DOCX)

large standard deviation

large mean

small sample size

small standard deviation

Question 5 If you were designing a study that would benefit from very disperse data points, you would want the input variable to have:

Homework Help:

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)

5DD. Changes in confidence interval based on changes in standard deviation or sample size (Links to an external site.) (DOCX)

a small margin of error

a large standard deviation

a large sample size

a large mean

MATH221 Statistics for Decision Making

Week 6 Homework

Question 1A consumer analyst reports that the mean life of a certain type of alkaline battery is more than 63 months. Write the null and alternative hypotheses and note which is the claim.

Homework Help:

6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)

Ho: ? ? 63, Ha: ? < 63 (claim)

Ho: ? = 63 (claim), Ha: ? ? 63

Ho: ? ? 63, Ha: ? > 63 (claim)

Ho: ? > 63 (claim), Ha: ? ? 63

Question 2A business claims that the mean time that customers wait for service is at most 5.9 minutes. Write the null and alternative hypotheses and note which is the claim.

Homework Help:

6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)

Ho: ? > 5.9 (claim), Ha: ? > 5.9

Ho: ? ? 5.9, Ha: ? ? 5.9 (claim)

Ho: ? ? 5.9 (claim), Ha: ? > 5.9

Ho: ? > 5.9, Ha: ? ? 5.9 (claim)

Question 3An amusement park claims that the average daily attendance is at least 20,000. Write the null and alternative hypotheses and note which is the claim.

Homework Help:

6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)

Ho: ? > 20000 (claim), Ha: ? = 20000

Ho: ? ? 20000, Ha: ? > 20000 (claim)

Ho: ? ? 20000 (claim), Ha: ? < 20000

Ho: ? = 20000, Ha: ? ? 20000 (claim)

Question 4A transportation organization claims that the mean travel time between two destinations is about 23 minutes. Write the null and alternative hypotheses and note which is the claim.

Homework Help:

6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)

Ho: ? > 23, Ha: ? ? 23 (claim)

Ho: ? ? 23, Ha: ? = 23 (claim)

Ho: ? = 23 (claim), Ha: ? ? 23

Ho: ? = 23 (claim), Ha: ? ? 23

Question 5If the null hypothesis is not rejected when it is false, this is called __________.

Homework Help:

6DB. Type I and type II errors (Links to an external site.) (DOCX)

the Empirical Rule

an alternative hypothesis

a type I error

a type II error

MATH221 Statistics for Decision Making

Week 7 Homework

Question 1Two variables have a negative non-linear correlation. Does the dependent variable increase or decrease as the independent variable increases?

Homework Help:

7DA. Linear, non-linear, positive and negative correlations (Links to an external site.) (PDF)

Dependent variable decreases

Dependent variable increases

Cannot determine from information given

Dependent variable would remain the same

Question 2What does the variable r represent?

Homework Help:

7DB. Correlation coefficient and coefficient of determination, notation and meanings (Links to an external site.) (PDF)

The coefficient of determination

The sample correlation coefficient

The population correlation coefficient

The critical value for the correlation coefficient

Question 3A golfer wants to determine if the type of driver she uses each year can be used to predict the amount of improvement in her game. Which variable would be the explanatory variable?

Homework Help:

7DA. Linear, non-linear, positive and negative correlations (Links to an external site.) (PDF)

7DC. Explanatory and response variables (Links to an external site.) (PDF)

The number of holes she plays

The improvement in her game

The type of driver

The rating of the golfer

Question 4Two variables have a positive linear correlation. Where would the y-intercept of the regression line be located on the y-axis?

Homework Help:

7DA. Linear, non-linear, positive and negative correlations (Links to an external site.) (PDF)

Below 0

To the left of 0

Cannot determine

To the right of 0

Question 5A value of the dependent variable that corresponds to the value of xi would be given the notation of:

Homework Help:

7DD. Regression notation of m, b, y1, x1, yi, xi, means of variables, estimates of variables (Links to an external site.) (PDF)

y1

b

m

yi

MATH221 Statistics for Decision Making

Week 3 Quiz

Question 1 (CO 1) Among 500 people at the concert, a survey of 35 found 28% found it too loud. What is the population and what is the sample?

Population: 500 at that concert; Sample: the 35 in the survey

Population: all concert goers; Sample: the 28% who found it too loud

Population: 500 at that concert: Sample: the 28% who found it too loud

Population: all concert goers; Sample: the 500 at that concert

Question 2(CO 1) A survey of 481 of your customers shows that 79% of them like the recent changes to the product. Is this percentage a parameter or a statistic and why?

Parameter as it represents the sample

Statistic as it represents the population

Parameter as it represents the population

Statistic as it represents the sample

Question 3(CO 1) Classify the data of the top grossing movies for 2017.

Statistics

Qualitative

Quantitative

Classical

Question 4(CO 1) The data set that lists the number of performances for each Broadway show in 2017 would be classified as what type of data?

Ratio

Nominal

Interval

Ordinal

Question 5(CO 1) A data set that includes the number of products that were produced within each hour by a company would be classified as what type of data?

Ordinal

Ratio

Nominal

Interval

Question 6(CO 1) What type of data collection might be best to estimate the impact of exercise on longevity?

Simulation

Experiment

Survey

Observational

Question 7(CO 1) What type of data collection might be best to study how voters might decide an upcoming ballot issue?

Simulation

Survey

Observational

Experiment

Question 8CO 1) You need to study the satisfaction of customers of a specific restaurant. You decide to randomly select one customer at each table. This would most closely describe which type of sampling technique?

Stratified

Random

Cluster

Systematic

Question 9(CO 1) Which of the following graphs would be a Pareto chart?

Vertical bars with spaces between with highest to left and shortest to right

Horizontal bars with various lengths

Vertical base with spaces between of various heights

Vertical bars with various lengths

Question 10(CO 1) In a normally distributed data set of how long customers stay in your store, the mean is 31.7 minutes and the standard deviation is 1.9minutes . Within what range would you expect 95% of your customers to stay in your store?

27.9-35.5

30.75-32.7

29.8-33.6

26.0-37.4

MATH221 Statistics for Decision Making

Week 5 Quiz

Question 1(CO 3) Consider the following table:

Age Group Frequency

18-29 983

30-39 784

40-49 686

50-59 632

60-69 541

70 and over 527

If you created the probability distribution for these data, what would be the probability of 30-39?

0.165

0.237

0.425

0.189

Question 2(CO 3) Consider the following table of hours worked by part-time employees. These employees must work in 5 hour blocks.

Weekly hours worked Probability

5 0.06

15 0.61

20 0.18

25 0.15

Find the mean of this variable.

12.20

17.50

18.95

16.80

Question 3(CO 3) Consider the following table.

Defects in batch Probability

0 0.30

1 0.28

2 0.21

3 0.09

4 0.08

5 0.04

Find the variance of this variable.

1.49

0.67

1.41

1.99

Question 4(CO 3) Consider the following table:

Defects in batch Probability

0 0.21

1 0.28

2 0.30

3 0.09

4 0.08

5 0.04

Find the standard deviation of this variable.

1.33

1.67

1.78

1.41

Question 5(CO 3) Twenty-two percent of US teens have heard of a fax machine. You randomly select 12 US teens. Find the probability that the number of these selected teens that have heard of a fax machine is exactly six (first answer listed below). Find the probability that the number is more than 8 (second answer listed below).

0.024, 0.001

0.993, 0.000

0.993, 0.024

0.024, 0.000

Question 6(CO 3) Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 85.2% of all their rugby balls have the correct shape. If exactly 7 of the 10 have the right shape, should the company stop the production line?

Yes, as the probability of seven having the correct shape is not unusual

Yes, as the probability of seven having the correct shape is unusual

No, as the probability of seven having the correct shape is not unusual

No, as the probability of seven having the correct shape is unusual

Question 7(CO 3) A bottle of water is supposed to have 12 ounces. The bottling company has determined that 98% of bottles have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled?

n=12, p=36, x=98

n=36, p=0.98, x=36

n=36, p=0.98, x=12

n=0, p=0.98, x=36

Question 8(CO 3) On the production line the company finds that 95.6% of products are made correctly. You are responsible for quality control and take batches of 30 products from the line and test them. What number of the 30 being incorrectly made would cause you to shut down production?

Less than 26

Less than 28

Less than 27

More than 25

Question 9(CO 3) The probability of someone ordering the daily special is 52%. If the restaurant expected 65 people for lunch, how many would you expect to order the daily special?

34

35

30

31

Question 10(CO 3) Fifty-seven percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?

0, 1, 8

1, 2, 8

1, 2, 8

0, 1, 2, 8

MATH221 Statistics for Decision Making

Week 7 Quiz

Question 1(CO 4) From a random sample of 55 businesses, it is found that the mean time that employees spend on personal issues each week is 4.9 hours with a standard deviation of 0.35 hours. What is the 95% confidence interval for the amount of time spent on personal issues?

(4.81, 4.99)

(4.84, 4.96)

(4.83, 4.97)

(4.82, 4.98)

Question 2(CO 4)If a confidence interval is given from 8.50 to 10.25 and the mean is known to be 9.375, what is the margin of error?

1.750

0.875

8.500

0.438

Question 3(CO 4) If the population standard deviation of a increases without other changes, what is most likely to happen to the confidence interval?

does not change

widens

cannot determine

narrows

Question 4(CO 4) From a random sample of 41 teens, it is found that on average they spend 43.1 hours each week online with a population standard deviation of 5.91 hours. What is the 90% confidence interval for the amount of time they spend online each week?

(37.19, 49.01)

(40.58, 45.62)

(31.28, 54.92)

(41.58, 44.62)

Question 5(CO 4) A company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a population standard deviation of 0.6 degrees, based on samples of 100. A sample of 100 refrigerators have an average temperature of 37.48 degrees. Are the refrigerators within the 90% confidence interval?

Yes, the temperature is within the confidence interval of (37.40, 37.60)

Yes, the temperature is within the confidence interval of (36.90, 38.10)

No, the temperature is outside the confidence interval of (36.90, 38.10)

No, the temperature is outside the confidence interval of (37.40, 37.60)

Question 6(CO 4) What is the 97% confidence interval for a sample of 104 soda cans that have a mean amount of 15.10 ounces and a population standard deviation of 0.08 ounces?

(15.940, 15.260)

(15.083, 15.117)

(12.033, 12.067)

(15.020, 15.180)

Question 7(CO 4) Determine the minimum sample size required when you want to be 98% confident that the sample mean is within two units of the population mean. Assume a population standard deviation of 5.75 in a normally distributed population.

45

23

43

44

Question 8(CO 4) Determine the minimum sample size required when you want to be 80% confident that the sample mean is within 1.5 units of the population mean. Assume a population standard deviation of 9.24 in a normally distributed population.

62

146

145

63

Question 9(CO 4) Determine the minimum sample size required when you want to be 75% confident that the sample mean is within thirty units of the population mean. Assume a population standard deviation of 327.8 in a normally distributed population

158

324

197

157

Question 10(CO 4) In a sample of 8 high school students, they spent an average of 28.8 hours each week doing sports with a sample standard deviation of 3.2 hours. Find the 95% confidence interval, assuming the times are normally distributed.

(25.62, 32.48)

(24.10, 34.50)

(26.12, 31.48)

(22.47, 35.21)

MATH221 Statistics for Decision Making

Week 2 LAB

Creating Graphs

1. Create a pie chart for the variable Car Color: Select the column with the Car variable, including the title of Car Color. Click on Insert, and then Recommended Charts. It should show a clustered column and click OK. Once the chart is shown, right click on the chart (main area) and select Change Chart Type. Select Pie and OK. Click on the pie slices, right click Add Data Labels, and select Add Data Callouts. Add an appropriate title. Copy and paste the chart here.

2. Create a histogram for the variable Height. You need to create a frequency distribution for the data by hand. Use 5 classes, find the class width, and then create the classes. Once you have the classes, count how many data points fall within each class. It may be helpful to sort the data based on the Height variable first. Once you have the classes and the frequency counts, put those data into the table in the Freq Distribution worksheet of the Week 1 Excel file. Copy and paste the graph here.

3. Create a scatter plot with the variables of height and money. Copy the height variable from the data file and paste it into the x column in the Scatter Plot worksheet of the week 1 Excel file. Copy the money variable from the data file and paste it into the y column. Copy and paste the scatter plot below.

Calculating Descriptive Statistics

4. Calculate descriptive statistics for the variable Height by Gender. Sort the data by gender by clicking on Data and then Sort. Copy the heights of the males form the data file into the Descriptive Statistics worksheet of the week 1 Excel file. Type the standard deviations below. These are sample data. Then from the data file, copy and paste the female data into the Descriptive Statistics workbook and do the same

 Mean Standard deviation Females Males

All answers should be complete sentences.

5. What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer.

6. What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer.

7. What is seen in the scatter plot for the height and money variables? Explain your answer.

8. Compare the mean for the heights of males and the mean for the heights of females in these data. Compare the values and explain what can be concluded based on the numbers.

9. Compare the standard deviation for the heights of males and the standard deviation for the heights of females in the class. Compare the values and explain what can be concluded based on the numbers.

10. Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated.

11. Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated.

MATH221 Statistics for Decision Making

Week 4 LAB

Calculating Binomial Probabilities

NOTE: For question 1, you will be using the same data file your instructor gave you for the Week 2 Lab.

1.Using the data file from your instructor (same one you used for the Week 2 Lab), calculate descriptive statistics for the variable (Coin) where each of the thirty-five students in the sample flipped a coin 10 times. Round your answers to three decimal places and type the mean and the standard deviation in the grey area below.

Plotting the Binomial Probabilities

? For the next part of the lab, open the Week 3 Excel worksheet. This will be used for the next few questions, rather than the data file used for the first question.

1. Click on the “binomial tables” workbook

2.Type in n=10 and p=0.5; this simulates ten flips of a coin where x is counting the number of heads that occur throughout the ten flips

3.Create a scatter plot, either directly in this spreadsheet (if you are comfortable with those steps), or by using the Week 1 spreadsheet and copying the data from here onto that sheet (x would be the x variable, and P(X=x) would be the y variable.

4. Repeat steps 2 and 3 with n=10 and p=0.25

5. Repeat steps 2 and 3 with n=10 and p=0.75

6. In the end, you will have three scatter plots for the first question below.

2. Create scatter plots for the binomial distribution when p=0.50, p=0.25, and p=0.75 (see directions above). Paste the three scatter plots in the grey area below.

Calculating Descriptive Statistics

Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions. Round all numeric answers to three decimal places.

3.List the probability value for each possibility in the binomial experiment calculated at the beginning of this lab, which was calculated with the probability of a success being ½. (Complete sentences not necessary; round your answers to three decimal places.)

P(x=0) P(x=6)

P(x=1) P(x=7)

P(x=2) P(x=8)

P(x=3) P(x=9)

P(x=4) P(x=10)

P(x=5)

4.Give the probability for the following based on the calculations in question 3 above, with the probability of a success being ½. (Complete sentences not necessary; round your answers to three decimal places.)

5.Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ½ and n = 10. Either show your work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =

6.Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¼ and n = 10. Write a comparison of these statistics to those from question 5 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =

7.Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¾ and n = 10. Write a comparison of these statistics to those from question 6 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =

8.Using all four of the properties of a Binomial experiment (see page 201 in the textbook) explain in a short paragraph of several complete sentences why the Coin variable from the class survey represents a binomial distribution from a binomial experiment.

9.Compare the mean and standard deviation for the Coin variable (question 1) with those of the mean and standard deviation for the binomial distribution that was calculated by hand in question 5. Explain how they are related in a short paragraph of several complete sentences.

MATH221 Statistics for Decision Making

Week 6 LAB

Scenario/Summary

Click to download the Week 6 Lab Document (Links to an external site.) to complete the lab for this week. All of the directions are included in the document.

The data for this lab is distributed by your professor.

The document includes places where you need to input the answers. Any place where you see a gray box is where you need to put an answer.

Deliverables

Each student will submit a lab. Below is the grading rubric for this assignment.

Category Points % Description

Questions 1-5 8 points each, 40 total 50% large and small sample confidence intervals for a mean

Question 6 16 points 20% normal probabilities compared with data outcomes

Question 7 24 points 30% normal probabilities compared with data outcomes

Total 80 points 100% A quality lab will meet or exceed all of the above requirements.

Required Software

Microsoft Office: Word and Excel

Use a personal copy or access the software at https://lab.devry.edu (Links to an external site.).

Lab Steps

Prepare and Submit Lab

Open Excel.

Open the lab Word document.

Follow the steps in the lab Word document to do calculations in Excel.

Copy and paste from Excel into the Word document or retype the answer, and then complete the answers to the questions in complete sentences (fill in each gray box in the Word document).

Save the lab Word document, and submit it; no other files should be submitted

Statistical Concepts:

· Data Simulation

· Confidence Intervals

· Normal Probabilities

All answers should be complete sentences.

We need to find the confidence interval for the SLEEP variable. To do this, we need to find the mean and standard deviation with the Week 1 spreadsheet. Then we can the Week 5 spreadsheet to find the confidence interval.

First, find the mean and standard deviation by copying the SLEEP variable and pasting it into the Week 1 spreadsheet. Write down the mean and the sample standard deviation as well as the count. Open the Week 5 spreadsheet and type in the values needed in the green cells at the top. The confidence interval is shown in the yellow cells as the lower limit and the upper limit.

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets.

Change the confidence level to 99% to find the 99% confidence interval for the SLEEP variable.

2. Give and interpret the 99% confidence interval for the hours of sleep a student gets.

3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs.

In the Week 2 Lab, you found the mean and the standard deviation for the HEIGHT variable for both males and females. Use those values for follow these directions to calculate the numbers again.

(From Week 2 Lab: Calculate descriptive statistics for the variable Height by Gender. Click on Insert and then Pivot Table. Click in the top box and select all the data (including labels) from Height through Gender. Also click on “new worksheet” and then OK. On the right of the new sheet, click on Height and Gender, making sure that Gender is in the Rows box and Height is in the Values box. Click on the down arrow next to Height in the Values box and select Value Field Settings. In the pop up box, click Averagethen OK. Write these down. Then click on the down arrow next to Height in the Values box again and select Value Field Settings. In the pop up box, click on StdDevthen OK. Write these values down.)

You will also need the number of males and the number of females in the dataset. You can either use the same pivot table created above by selecting Count in the Value Field Settings, or you can actually count in the dataset.

Then use the Week 5 spreadsheet to calculate the following confidence intervals. The male confidence interval would be one calculation in the spreadsheet and the females would be a second calculation.

4. Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?

5. Give and interpret the 99% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?

6. Find the mean and standard deviation of the DRIVE variable by copying that variable into the Week 1 spreadsheet. Use the Week 4 spreadsheet to determine the percentage of data points from that data set that we would expect to be less than 40. To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points. That is the actual percentage. How does this compare with your prediction?

 Mean ______________ Standard deviation ____________________ Predicted percentage ______________________________ Actual percentage _____________________________ Comparison ___________________________________________________ ______________________________________________________________

7. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Use the Week 4 spreadsheet again to find the percentage of the data set we expect to have values between 40 and 70 as well as for more than 70. Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set. How do each of these compare with your prediction and why is there a difference?

 Predicted percentage between 40 and 70 ______________________________ Actual percentage _____________________________________________ Predicted percentage more than 70 miles ________________________________ Actual percentage ___________________________________________ Comparison ____________________________________________________ _______________________________________________________________ Why? __________________________________________________________ ________________________________________________________________

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