MATH221 Statistics for Decision Making
Week 1 Homework
Question 1The age of every fourth person entering a department store. The selected individuals would be considered a:
Statistic
Parameter
Population
Correct!
Sample
Question 2 In a survey of 1000 adults, 34% found they prefer charcoal to gas grills. The 1000 would be considered a:
Sample
Population
Parameter
Statistic
Question 3Inferential statistics is when sample data is used to:
Influence a decision maker
Calculate a mean
Say something about the population
Determine when an event is most likely to occur
Question 4The milligrams of tar in 30 cigarettes would be considered:
Interval data
Ratio data
Ordinal data
Nominal data
Question 5If a data set included the color of cars in a parking lot, those data would be considered:
Quantitative data
Ratio data
Qualitative data
Interval data
MATH221 Statistics for Decision Making
Week 2 Homework
Question 1A student believes that there is a 90% probability of getting an A on the next test. This would be considered:
Empirical probability
Manufactured probability
Subjective probability
Classical probability
Question 2Given the following information, find the probability that a randomly selected student will be tall, but not very tall. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21
50.5%
39.4%
10.1%
49.5%
Question 3Given 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
46.9%
58.0%
39.5%
60.5%
Question 4Given that there is a 28% 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?
20.2%
14.5%
5.6%
34.7%
Question 5Consider the following table. What is the probability of blue?
Red Blue Green Total
Yes 33 44 14 91
No 18 5 28 51
Total 51 49 42 142
44/49
91/142
49/142
51/142
Question 6Consider the following table. What is probability of yes, given green?
Red Blue Green Total
Yes 33 44 14 91
No 18 5 28 51
Total 51 49 42 142
14/91
14/42
51/142
42/142
MATH221 Statistics for Decision Making
Week 3 Homework
Question 1Let x represent the number of cars in a parking lot. This would be considered what type of variable:
Discrete
Nonsensical
Continuous
Lagging
Question 2 Let x represent the inches of rain on crops in Akron, Ohio. This would be considered what type of variable:
Continuous
Discrete
Inferential
Distributed
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?
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) 0.10
41-50 (average=43) 0.74
51 and over (average=54) 0.08
Find the mean of this variable.
39.0
31.8
41.6
25.2
Question 5Consider the following table.
Defects in batch Probability
0 0.28
1 0.35
2 0.16
3 0.09
4 0.10
5 0.02
Find the variance of this variable.
0.85
1.44
1.35
1.83
MATH221 Statistics for Decision Making
Week 4 Homework
Question 1The 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 6 minutes to select a shoe purchase. Is this outcome unusual?
Probability is 0.09, which is unusual as it is less than 5%
Probability is 0.91, which is usual as it is greater than 5%
Probability is 0.09, which is usual as it is not less than 5%
Probability is 0.91, which is unusual as it is greater than 5%
Question 2Monthly 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 $165, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?
Probability is 0.06, which is unusual as it is not less than 5%
Probability is 0.06, which is usual as it is not less than 5%
Probability is 0.94, which is usual as it is greater than 5%
Probability is 0.94, which is unusual as it is greater than 5%
Question 3In 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.
0.40
Less than 1%
0.70
0.30
Question 4A 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 0.70mm. Would this outcome warrant a refund (meaning that it would be unusual)?
Probability of 0.79 and would not warrant a refund
Probability of 0.79 and would warrant a refund
Probability of 0.21 and would not warrant a refund
Probability of 0.21 and would warrant a refund
Question 5A 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 2.81 minutes.
0.818
0.636
0.182
0.018
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?
(19.24, 24.14)
(20.71, 22.67)
(21.78, 22.60)
(20.86, 22.52)
Question 2If 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?
4.54
9.07
18.14
43.83
Question 3If a computer manufacturer needed a supplier that could produce parts that were very precise, what characteristics would be better?
wide confidence interval with high confidence level
narrow confidence interval at high confidence level
narrow confidence interval at low confidence level
wide confidence interval with low confidence level
Question 4Which of the following are most likely to lead to a wide confidence interval?
large sample size
small standard deviation
large mean
large standard deviation
Question 5If you were designing a study that would benefit from a narrow range of data points, you would want the input variable to have:
a small mean
a small sample size
a large standard deviation
a small margin of error
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 no more than 36 months. Write the null and alternative hypotheses and note which is the claim.
Ho: μ ≤ 36, Ha: μ > 36 (claim)
Ho: μ > 36, Ha: μ ≤ 36 (claim)
Ho: μ ≤ 36 (claim), Ha: μ > 36
Ho: μ = 36 (claim), Ha: μ ≥ 36
Question 2A business claims that the mean time that customers wait for service is at most 9.2 minutes. Write the null and alternative hypotheses and note which is the claim.
Ho: μ ≥ 9.2, Ha: μ ≤ 9.2 (claim)
Ho: μ > 9.2, Ha: μ ≤ 9.2 (claim)
Ho: μ > 9.2 (claim), Ha: μ > 9.2
Ho: μ ≤ 9.2 (claim), Ha: μ > 9.2
Question 3An amusement park claims that the average daily attendance is at least 15,000. Write the null and alternative hypotheses and note which is the claim.
>Ho: μ ≥ 15000 (claim), Ha: μ < 15000
Ho: μ = 15000, Ha: μ ≤ 15000 (claim)
Ho: μ ≤ 15000, Ha: μ > 15000 (claim)
Ho: μ > 15000 (claim), Ha: μ = 15000
Question 4A transportation organization claims that the mean travel time between two destinations is about 12 minutes. Write the null and alternative hypotheses and note which is the claim.
Ho: μ = 12 (claim), Ha: μ ≤ 12
Ho: μ = 12 (claim), Ha: μ ≠ 12
Ho: μ > 12, Ha: μ ≤ 12 (claim)
Ho: μ ≠ 12, Ha: μ = 12 (claim)
Question 5 Type I and type II errors occur because of what issue within the hypothesis testing process?
The population is not a representative subset of the sample
The sample mean is different than the population mean
The sample taken is not representative of the population
The math calculations were done incorrectly
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?
Dependent variable decreases
Dependent variable increases
Cannot determine from information given
Dependent variable would remain the same
Question 2What does the variable ρ represent?
The critical value for the correlation coefficient
The coefficient of determination
The sample correlation coefficient
The population correlation coefficient
Question 3A baseball player wants to determine if the type of bat he uses each year can be used to predict the amount of improvement in his game. Which variable would be the response variable?
The improvement in his game
The number of times he bats
The type of bat
The baseball player
Question 4Two variables have a negative linear correlation. Where would the y-intercept of the regression line be located on the y-axis?
To the right of 0
To the left of 0
Cannot determine
Below 0
Question 5A value of the dependent variable that corresponds to the value of xi would be given the notation of:
b
yi
m
y1
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
This is the time to start preparing for the Reflection paper at the end of the course. As such the discussions will take on a different tone/format for weeks 6 and 7. The posts will consist of
ANALYTICAL: Describe how you could use Hypothesis Testing to serve the needs of a decision-making process in your current job, a past job, or life situation.
GRAPHICAL: Identify two (2) options for graphically representing the data from your ANALYTICAL POST to present to decision-makers and assess the pros and cons of each graphical option.
ENGAGEMENT: Extend the conversation of another students ANALYTICAL or GRAPHICAL POST by offering another analytical method or set of graphical options.
MATH221 Statistics for Decision Making
Week 7 Discussion
REGRESSION
This is the time to start preparing for the Reflection paper at the end of the course. As such the discussions will take on a different tone/format for weeks 6 and 7. The posts will consist of
ANALYTICAL: Describe how you could use Linear Regression to serve the needs of a decision-making process in your current job, a past job, or life situation.
GRAPHICAL: Identify two (2) options for graphically representing the data from your ANALYTICAL POST to present to decision-makers and assess the pros and cons of each graphical option.
ENGAGEMENT: Extend the conversation of another students ANALYTICAL or GRAPHICAL POST by offering another analytical method or set of graphical options.
MATH221 Statistics for Decision Making
Week 3 Quiz
Question 1 (CO 1) A survey of 385 people who like wild sweaters found that 74% had a wild holiday sweater. What is the population and what is the sample?
Population: people who like wild sweaters; Sample: the 74% that had a wild holiday sweater
Population: people who like wild sweaters: Sample: the 385 people who had a wild holiday sweater
Population: people who like wild sweaters; Sample: the 385 people who like wild sweaters
Population: people who like sweaters; Sample: the 74% that had a wild holiday sweater
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 population
Statistic as it represents the population !
Statistic as it represents the sample
Parameter as it represents the sample
Question 3 (CO 1) Classify the data of the top grossing movies for 2017.
Classical
Statistics
Quantitative
Qualitative
Question 4 (CO 1) The data set that lists the runs scored at each of the weekend’s baseball games would be classified as what type of data?
Interval
Ratio
Nominal
Ordinal
Question 5 (CO 1) A data set that includes the years in which your hometown team won championships would be classified as what type of data:
Ratio
Ordinal
Interval
Nominal
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?
0.425
0.237
Correct!
0.189
0.165
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 0.15
15 0.28
20 0.31
25 0.26
Find the mean of this variable.
17.50
20.60
17.65
18.95
Question 3 (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 variance of this variable.
1.67
1.78
1.99
1.33
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.
1.41
1.67
1.33
1.78
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).
0.993, 0.024
0.024, 0.001
0.993, 0.000
0.024, 0.000
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 5.8 hours with a standard deviation of 0.35 hours. What is the 95% confidence interval for the amount of time spent on personal issues?
(5.71, 5.89)
(5.74, 5.90)
(5.72, 5.88)
(5.73, 5.87)
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?
8.500
1.750
0.875
0.438
Question 3 (CO 4) Which of the following is most likely to lead to a large margin of error?
large sample size
small sample size
small standard deviation
small mean
Question 4 (CO 4) From a random sample of 41 teens, it is found that on average they spend 31.8 hours each week online with a population standard deviation of 3.65 hours. What is the 90% confidence interval for the amount of time they spend online each week?
(28.15, 35.45)
(24.50, 39.10)
(30.86, 32.74)
(29.99, 33.61)
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 37.37 degrees. Are the refrigerators within the 90% confidence interval?
Yes, the temperature is within the confidence interval of (37.40, 37.60)
No, the temperature is outside the confidence interval of (36.90, 38.10)
Yes, the temperature is within the confidence interval of (36.90, 38.10)
No, the temperature is outside the confidence interval of (37.40, 37.60)
MATH221 Statistics for Decision Making
Week 8 Assignment
Reflection Paper
Complete the following by writing a response to three of the four following questions. For each question, your response should be 2 or more paragraphs. Make it clear which question you are answering and use correct grammar throughout. If you answer all four questions, only the first three provided will be graded.
Your responses are to be based on your own experiences and insights. Do not use materials and examples from other sources, including the Internet. Students have used examples from outside sources in the past and have failed this final assessment and in some cases, failed the course due to evidence of plagiarism.
Describe how you could use hypothesis testing to help make a decision in your current job, a past job, or a life situation. Include a description of the decision, what would be the null and alternative hypotheses, and how data could ideally be collected to test the hypotheses.
Describe how you could use confidence intervals to help make a decision in your current job, a past job, or life situation. Include a description of the decision, how the interval would impact the decision, and how data could ideally be collected to determine the interval.
Describe how you could use regression analysis to help make a decision in your current job, a past job, or a life situation. Include a description of the decision, what would be the independent and dependent variables, and how data could ideally be collected to calculate the regression equation.
Describe a data set that you have encountered or could envision that would be applicable to your current job, a past job, or a life situation. Identify two (2) options for graphically representing those data to present to decision-makers, such a pie charts, time series, Pareto charts, histograms, etc. Assess the pros and cons of each graphical option.
MATH221 Statistics for Decision Making
Week 2 LAB
Instructions-BEGIN
? Data have already been formatted and entered into an Excelworksheet.
? Obtain the data file for this lab from your instructor.
? Use the Week 1 spreadsheet (available from the top of the Week 1 Lesson) for graphs and calculations. You will need to copy data from the data file into the calculations spreadsheet to answer some questions.
? The names of each variable from the survey are in the first row of the Worksheet. This row has a background color of gray to identify it as the variable names. All other rows of the Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. On page 6 of this lab, you will find a code sheetthat identifies the correspondence between the variable names and the survey questions.
? Follow the directions below and then paste the graphs from Excel in the grey areas for question 1 through 3. You will be using the Week 1 Excel Sheet for many of the calculations. Type your answers to questions 4 through 11 where noted in the grey areas. When asked for explanations, please give thorough, multi-sentence or paragraph length explanations.
? The completed Lab Word Document with your responses to the 11 questions will be the ONE and only document submitted to the Week 2:Lab. When saving and submitting the document, you are required to use the following format: Last Name_ First Name_Week2Lab.
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 scatter plot with the variables of Drive and Money. Copy the Drive 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.
- 3. Create a histogram for the variable Drive.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 Drive 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.
- 4. Calculate descriptive statistics for the variable Sleep by Gender. Sort the data by gender by clicking on Data and then Sort. Copy the Sleep of the males from the data file into the Descriptive Statistics worksheet of the Week 1 Excel file. Type the mean and standard deviation below.These are sample data. Then, copy and paste the female data into the Descriptive Statistics workbook and do the same. Keep three decimal places.
- 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 scatter plot for the Drive and Money variables? Explain your answer.
- 7. What is seen in the histogram created for the driving distance of students in this class (include the shape)? Explain your answer.
- 8. Compare the mean hours of sleep for males and the mean for females in these data. Compare the values and explain what can be concluded based on the numbers.
- 9. Compare the standard deviation for the sleep of males and the standard deviation for the sleep 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 sleep amounts should be between what two values? Either show work or explain how your answer was calculated.
- 11. Using the empirical rule, 68% of male sleep amounts should be between what two values? Either show work or explain how your answer was calculated.
MATH221 Statistics for Decision Making
Week 4 LAB
- 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 typethe 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 Excelworksheet. 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=0.10
5. Repeat steps 2 and 3 with n=10 and p=0.90
6. In the end, you will have three scatter plots for the first question below.
- Create scatter plots for the binomial distribution when p=0.50, p=0.10, and p=0.90 (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 sentence not necessary; round your answers to three decimal places)
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P(x=0)
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P(x=6)
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P(x=1)
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P(x=7)
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P(x=2)
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P(x=8)
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P(x=3)
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P(x=9)
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P(x=4)
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P(x=10)
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P(x=5)
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Give the probability for the following based on the calculations in question 3 above, with the probability of a success being ½. (Complete sentence not necessary; round your answers to three decimal places)
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P(x≥2)
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P(x<0)
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P(x>2)
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P(x≤5)
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P(5<x ≤7)
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P(x<5 or x≥7)
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5. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being 0.50and n = 10. Either show 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 0.10 and n = 10. Write a comparison of these statistics to those from question 5in 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 0.90and n = 10. Write a comparison of these statistics to those from question 6in 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
In the Week 2 Lab, you found the mean and the standard deviation for the SLEEP 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 Sleep by Gender. Sort the data by gender by clicking on Data and then Sort. Copy the Sleep of the males from the data file into the Descriptive Statistics worksheet of the Week 1 Excel file.[Write down the mean and standard deviation.] These are sample data. Then, copy and paste the female data into the Descriptive Statistics workbook and do the same. Keep three decimal places.)
You will also need the number of males and the number of females in the dataset. You can actually count these 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.
- Give and interpret the 95% confidence intervals for males and a second 95% confidence interval for females on the SLEEP variable. Which is wider and why?
- Give and interpret the 99% confidence intervals for males and a second 99% confidence interval for females on the SLEEP variable. Which is wider and why?
We need to find the confidence interval for the SHOE SIZE 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. This does not need to be separated by males and females, rather one interval for the entire data set.
First, find the mean and standard deviation by copying the SHOE SIZE 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 to find the confidence interval.
3. Give and interpret the 95% confidence interval for the size of students’ shoes.
Change the confidence level to 99% to find the 99% confidence interval for the SHOE SIZE variable.
4. Give and interpret the 99% confidence interval for the size of students’ shoes.
5. Compare the 95% and 99% confidence intervals for the size of students’ shoes. Explain the difference between these intervals and why this difference occurs.
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 25. To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 25 out of the total 35 data points. That is the actual percentage. How does this compare with your prediction?
7. What percentage of data would you predict would be between 25 and 50 and what percentage would you predict would be more than 50 miles? Use the Week 4 spreadsheet again to find the percentage of the data set we expect to have values between 25 and 50 as well as for more than 50. Now determine the percentage of data points in the dataset that fall within each of these ranges, 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?
