MATH221 Statistics for Decision Making
Week 1 Discussion
Descriptive Statistics
In these discussions, exploration is encouraged!
Each week you must post 3 times (details below):
(Required) Create and post a response that fully answers one of the 10 questions below (no later than Wednesday)
(Required) Create and post a response that fully answers a different one of the 10 questions below (on a different day)
(Required) Post one quality response to another classmates' "main" post or to a professor post (by the end of the week).
(Required) The posts must be submitted on at least 3 different days.
(Optional) Additional posts and/or days of participation are not required, but are certainly welcome!
NOTE: Always paste the question itself (and its number) above your answer (or enough of it, when it's a really long question, to make it clear which one you are addressing).
For full posting guidelines, review the Real World Discussions: Requirements page.
1. Different Charts
1. Describe the difference between bar charts, histograms, Pareto charts, including how they are structured and in what situations are each most effectively used?
2. Histogram - 4 Classes
2. Given the following data points, describe the steps to create a histogram with 4 classes.
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3. Histogram - 3 Classes
3. Given the following data points, describe the steps to create a histogram with 3 classes.
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4. Histogram - 5 Classes
4. Given the following data points, describe the steps to create a histogram with 5 classes.
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5. Male and Female Groups
5. Describe the steps and then find x¯ and s of the males and of the females as separate groups. Compare these values.
Females: 43 48 54 55 33 48 62 68 54 61
Males: 62 55 54 59 21 22 50 59 62 38
6. Male and Female Medians
6. Describe the steps and then find x¯ and the median of males and of the females as separate groups. Compare these values.
Females: 43 48 54 55 33 48 62 68 54 61
Males: 62 55 54 59 21 22 50 59 62 38
7. Sample versus Population
7. Describe the steps and then find s and σ with different assumptions regarding the data. Compare and discuss the differences.
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8. Empirical Rule
8. Use the Empirical Rule to find the 68% range and find the percentage of data points in that range.
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9. The 95% Range
9. Use the Empirical Rule to find the 95% range and find the percentage of data points in that range.
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10. Ethics! (Graphs, misleading?)
10. Ethics: Find a graph or chart in the news and describe the information provided. Was this graph the best choice for presenting the data? Why or why not? How might the graph mislead the reader, if at all?
MATH221 Statistics for Decision Making
Week 2 Discussion
Probabilities
In these discussions, exploration is encouraged!
Each week you must post 3 times (details below):
(Required) Create and post a response that fully answers one of the 10 questions below (no later than Wednesday)
(Required) Create and post a response that fully answers a different one of the 10 questions below (on a different day)
(Required) Post one quality response to another classmates' "main" post or to a professor post (by the end of the week).
(Required) The posts must be submitted on at least 3 different days.
(Optional) Additional posts and/or days of participation are not required, but are certainly welcome!
NOTE: Always paste the question itself (and its number) above your answer (or enough of it, when it's a really long question, to make it clear which one you are addressing).
For full posting guidelines, review the Real World Discussions: Requirements page.
1. Contingencies
1. Create a contingency table with two variables. Then pose two conditional probability questions for others to solve. Here is an example (do not use this one). Other students can reply with details on how to find the conditional probabilities.
|
Red
|
Green
|
Blue
|
TOTAL
|
|
|
Large
|
10
|
2
|
18
|
30
|
|
Medium
|
12
|
16
|
4
|
32
|
|
Small
|
8
|
10
|
6
|
24
|
|
TOTAL
|
30
|
28
|
28
|
86
|
What is the P(blue|medium)?
What is the P(small|green)?
2. Frequency Distribution 1
2. Use the following frequency distribution to determine the P(x<2) and P’(x<2). Please note that these are complements of each other. Describe your thought process and/or show work!
|
Number of cars
|
Frequency
|
|
0
|
128
|
|
1
|
243
|
|
2
|
286
|
|
3
|
151
|
|
4
|
84
|
|
5+
|
32
|
3. Real-Life Probability Example
3. Give an example of a probability distribution in your home life or in your career. Is this used directly or indirectly, such as what protein to make for dinner? Provide the example and an estimate of the probability distribution.
4. One Event... Impacts Another?
4. How might the occurrence of one event in your life or career impact the probabilities of another event? Are these events independent or dependent? Why?
5. Probability for Quality Control
5. Thinking of a manufacturing company, how might probability be a part of their quality control? Which companies might consider more outcomes as “unusual” based on the sensitivity of what they produce? Why?
6. Frequency Distribution 2
6. Use the following frequency distribution to determine the P(1 < x < 4) and P(1 ≤ x ≤ 4). Describe your thought process and/or show work!
|
Number of cars
|
Frequency
|
|
0
|
128
|
|
1
|
243
|
|
2
|
286
|
|
3
|
151
|
|
4
|
84
|
|
5+
|
32
|
7. Frequency Distribution 3
7. Use the following frequency distribution to determine the P(x < 0) and P(x ≥ 3). Describe your thought process and/or show work!
|
Number of cars
|
Frequency
|
|
0
|
128
|
|
1
|
243
|
|
2
|
286
|
|
3
|
151
|
|
4
|
84
|
|
5+
|
32
|
8. Probability Distribution in the News
8. Find an example of a probability distribution in the news. Why was this presented? What decisions might it impact?
9. Ethics! (Misinterpretation?)
9. Ethics: Find an example of a probability in the news that might be misinterpreted by the reader. How might it have been presented more directly, or in a way that would lead to less misinterpretation?
10. Ethics! (Reasonable?)
10. Ethics: Find an example of a conditional probability in the news. Was the occurrence of the first event reasonable? Why or why not?
MATH221 Statistics for Decision Making
Week 3 Discussion
Discrete Probability Variables
In these discussions, exploration is encouraged!
Each week you must post 3 times (details below):
(Required) Create and post a response that fully answers one of the 10 questions below (no later than Wednesday)
(Required) Create and post a response that fully answers a different one of the 10 questions below (on a different day)
(Required) Post one quality response to another classmates' "main" post or to a professor post (by the end of the week).
(Required) The posts must be submitted on at least 3 different days.
(Optional) Additional posts and/or days of participation are not required, but are certainly welcome!
NOTE: Always paste the question itself (and its number) above your answer (or enough of it, when it's a really long question, to make it clear which one you are addressing).
For full posting guidelines, review the Real World Discussions: Requirements page.
1. Show the calculation...
1. Show the calculation to find the μ and σ of a binomial variable whose probability of success if 0.3 with a total number of attempts of 20.
2. Probability of Success...
2. Show the calculation to find the μ and σ of a binomial variable whose probability of success if 0.7 with a total number of attempts of 40.
3. Different Probabilities of Success
3. Show the calculation to find the μ and σ of a binomial variable with a total number of attempts of 30 with first with the probability of success of 0.2 and then again with the probability of success of 0.8. Compare and discuss the differences.
4. Graph Distribution 1
4. Graph the entire distribution of a binomial variable whose probability of success if 0.3 with a total number of attempts of 20.
5. Graph Distribution 2
5. Graph the entire distribution of a binomial variable whose probability of success if 0.7 with a total number of attempts of 40.
6. Eat 2 M&Ms
6. There are 10 M&Ms of which 6 are green, in a bowl. You select 2 of them and eat each after it is selected. Is this a binomial experiment? Why or why not?
7. Put the M&Ms Back!
7. There are 10 M&Ms of which 6 are green, in a bowl. You select 2 of them and putting each back in the bowl after it is selected. Is this a binomial experiment? Why or why not?
8. Binomial Experiment Situation
8. Describe a situation that would result in a binomial experiment. Relate to each part of that situation to the definition of a binomial experiment.
9. Solve Binomial Probability
9. Use the binomial experiment that a peer described in their response question #8. From that, create and solve a binomial probability. You may need to make a few assumptions, which is fine.
10. Ethics! (Be honest)
10. Ethics: Describe a situation where using a binomial probability with only two outcomes would be misleading. What would make that use misleading and how might it be presented more effectively (honestly)?
MATH221 Statistics for Decision Making
Week 4 Discussion
Interpreting Normal Distributions
In these discussions, exploration is encouraged!
Each week you must post 3 times (details below):
(Required) Create and post a response that fully answers one of the 10 questions below (no later than Wednesday)
(Required) Create and post a response that fully answers a different one of the 10 questions below (on a different day)
(Required) Post one quality response to another classmates' "main" post or to a professor post (by the end of the week).
(Required) The posts must be submitted on at least 3 different days.
(Optional) Additional posts and/or days of participation are not required, but are certainly welcome!
NOTE: Always paste the question itself (and its number) above your answer (or enough of it, when it's a really long question, to make it clear which one you are addressing).
For full posting guidelines, review the Real World Discussions: Requirements page.
1. Estimated versus Actual 1
1. Using these 20 data points from a normal distribution, find their μ and σ. Then find P(x<20). Compare that probability with the percent of the 20 data points that are below 20.
22.1 30.9 18.6 34.7 15.3 37.1 40.8 33.9 40.8 18.1 15.1 32.6 30.3 28.3 28.3 23.1 28.4 20.7 25.1 22.1
2. Estimated versus Actual 2
2. Using these 20 data points from a normal distribution, find their μ and σ. Then find P(20<x<35). Compare that probability with the percent of the 20 data points that are between 20 and 35.
22.1 30.9 18.6 34.7 15.3 37.1 40.8 33.9 40.8 18.1 15.1 32.6 30.3 28.3 28.3 23.1 28.4 20.7 25.1 22.1
3. Daily Life Variable - Normal Distribution
3. Give an example of a normally distributed variable that is found within your daily life. Describe why it is a normally distributed variable.
4. Daily Life Variable - Right Skewed
4. Give an example of a variable with a right skewed distribution that is found within your daily life. Describe why it has a right skewed distribution.
5. Daily Life Variable - Left Skewed
5. Give an example of a variable with a left skewed distribution that is found within your daily life. Describe why it has a left skewed distribution.
6. Discrete or Continuous? ...Students
6. Describe why each of these variables is either discrete or continuous: Number of students in a live lesson and the length of the live lesson
7. Discrete or Continuous? ...Lettuce
7. Describe why each of these variables is either discrete or continuous: Amount of lettuce taken from salad bar and number of customers in store.
8. Discrete or Continuous? ...Paint Cans
8. Describe why each of these variables is either discrete or continuous: Paint cans sold and paint used to cover walls.
9. Discrete or Continuous? ...Milk & Cookies
9. Describe why each of these variables is either discrete or continuous: Milk spilled and cookies dropped
10. Ethics! (Does .5+.5 = 1?)
10. Ethics: Consider a manufacturing company that is counting the number of products completed. Consider that there were two products that were both half done and the company included the two halves as one additional completion in its count of products completed. What would be your argument for or against this presentation?
MATH221 Statistics for Decision Making
Week 5 Discussion
Confidence Interval Concepts
In these discussions, exploration is encouraged!
Each week you must post 3 times (details below):
(Required) Create and post a response that fully answers one of the 10 questions below (no later than Wednesday)
(Required) Create and post a response that fully answers a different one of the 10 questions below (on a different day)
(Required) Post one quality response to another classmates' "main" post or to a professor post (by the end of the week).
(Required) The posts must be submitted on at least 3 different days.
(Optional) Additional posts and/or days of participation are not required, but are certainly welcome!
NOTE: Always paste the question itself (and its number) above your answer (or enough of it, when it's a really long question, to make it clear which one you are addressing).
For full posting guidelines, review the Real World Discussions: Requirements page.
1. Find a Survey or Poll... Confidence Interval
1. Look in the newspapers, magazines, or other news sources for results of a survey or poll that show the confidence interval, usually as a +/- 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?
2. Confidence Intervals ...Sample
2. Calculate the 90% and 95% confidence intervals of the following data set assuming this is sample data. Describe your process as well as the difference in the intervals.
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3. Confidence Intervals ...Population
3. Calculate the 90% and 95% confidence intervals of the following data set assuming this is population data. Describe your process as well as the difference in the intervals.
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4. Why?
4. Why are sample and population confidence intervals calculated differently?
5. Teenagers DO Eat Pizza!
5. Say that on average teenagers eat 10 slices of pizza each week, with a 95% confidence interval of (8-12). We take a sample of teenagers and find that this group eats an average of 6 slices each week. What can we say about the teenagers in the sample in relation to the confidence interval?
6. Impact of Differences
6. Calculate and show the 95% confidence interval for males and females separately. What impact are the different means having on the intervals and what impact are the different standard deviations having?
Females: 43 48 54 55 33 48 62 68 54 61
Males: 62 75 54 59 21 22 50 59 62 38
7. More Weekly Pizza!
7. Say that on average teenagers eat 10 slices of pizza each week, with a 95% confidence interval of (8-12). We take a sample of teenagers and find that this group eats an average of 9 slices each week. What can we say about the teenagers in the sample in relation to the confidence interval?
8. Minimum Sample Size
8. Describe the process of finding the minimum sample size for a given level of confidence and a given margin of error. Describe a situation where finding the minimum sample size would be helpful.
9. Distribution Shapes
9. Describe the difference in the shape and nature of the t and z distributions. In what ways are they the same? Do they change in shape? If so, what causes the change? If not, why not?
10. Ethics! (Decisions, Decisions)
10. Ethics: Describe a decision you might have made in the past or might make in the future where knowing a confidence interval would/could have helped you in making that decision. How might the interval improve or detract from the decision?
MATH221 Statistics for Decision Making
Week 6 Discussion
Hypotheses in the Real World
In these discussions, exploration is encouraged!
Each week you must post 3 times (details below - ALSO - See Special Instructions for Questions 1-9):
(Required) Create and post a response that fully answers one of the 10 questions below (no later than Wednesday)
(Required) Create and post a response that fully answers a different one of the 10 questions below (on a different day)
(Required) Post one quality response to another classmates' "main" post or to a professor post (by the end of the week).
(Required) The posts must be submitted on at least 3 different days.
(Optional) Additional posts and/or days of participation are not required, but are certainly welcome!
NOTE: Always paste the question itself (and its number) above your answer (or enough of it, when it's a really long question, to make it clear which one you are addressing).
Special Instructions for Questions 1-9:
Select a problem below. For your first post, complete the following steps:
a. identify the claim and state H0 and Ha.
b. find the standardized test statistic z or t OR find the corresponding P-value.
c. Identify the type of test. Compare the p-value with α OR the standardized test statistic with the critical value of z or t
For your second post, reply to another student’s first post and complete the problem with these steps:
d. decide whether to reject or fail to reject the null hypothesis. based on the test statistic or the p-value
e. interpret the decision in the context of the original claim.
For your subsequent posts, consider another way to look at the problem, respectfully propose a different structure or response, or use the same problem changing one element (e.g., number in sample, standard deviation, or claim) to post it again.
For full posting guidelines, review the Real World Discussions: Requirements page.
1. A Random Sample of...
1. A random sample of 100 medical school applicants at a university has a mean total score of 502 on the MCAT. According to a report, the mean total score for the school’s applicants is more than 499. Assume the population standard deviation is 10.6. At α = 0.01, is there enough evidence to support the report’s claim? (Source: Association of American Medical Colleges)
2. Sprinkler Systems
2. Sprinkler Systems: A manufacturer of sprinkler systems designed for fire protection claims that the average activating temperature is at least 135°F. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133°F. Assume the population standard deviation is 3.3°F. At α = 0.10, do you have enough evidence to reject the manufacturer’s claim?
3. Boston Marathon
3. Boston Marathon: A sports statistician claims that the mean winning times for Boston Marathon women’s open division champions is at least 2.68 hours. The mean winning time of a sample of 30 randomly selected Boston Marathon women’s open division champions is 2.60 hours. Assume the population standard deviation is 0.32 hour. At α = 0.05, can you reject the claim? (Source: Boston Athletic Association)
4. A Consumer Group Claims...
4. A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is 6.3 seconds. A random sample of 33 sedans has a mean acceleration time from 0 to 60 miles per hour of 7.2 seconds. Assume the population standard deviation is 2.5 seconds. At α = 0.05, can you reject the claim? (Source: Zero to 60 Times)
5. Caffeine Content
5. Caffeine Content: A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty-six 12-ounce bottles of caffeinated soft drinks has a mean caffeine content of 36.4 milligrams. Assume the population standard deviation is 10.8 milligrams. At α = 0.01, can you reject the research organization’s claim? (Source: National Soft Drink Association)
6. Fast Food
6. Fast Food: A fast-food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 920 milligrams. A random sample of 44 breakfast sandwiches has a mean sodium content of 925 milligrams. Assume the population standard deviation is 18 milligrams. At α = 0.10, do you have enough evidence to reject the restaurant’s claim?
7. Light Bulbs
7. Light Bulbs: A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 750 hours. A random sample of 25 light bulbs has a mean life of 745 hours. Assume the population is normally distributed and the population standard deviation is 60 hours. At α = 0.02, do you have enough evidence to reject the manufacturer’s claim?
8. Used Car Cost8. Used Car Cost: A used car dealer says that the mean price of a three-year-old sport utility vehicle (in good condition) is $20,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $20,640 and a standard deviation of $1990. Is there enough evidence to reject the claim at α = 0.05?
9. DMV Wait Times
9. DMV Wait Times: A state department of Transportation claims that the mean wait time for various services at its different locations is at most 6 minutes. A random sample of 34 services at different locations has a mean wait time of 10.3 minutes and a standard deviation of 8.0 minutes. Is there enough evidence to reject the claim at α = 0.01?
10. Ethics! (How it's stated?)
10. Ethics: Which hypothesis, the null or the alternative, is easiest for the math to support? Knowing that, could someone state their hypothesis so that it is the most likely to be supported? Should every hypothesis test be done with various wordings of the claim, or is there a structure to the hypotheses that should be followed?
MATH221 Statistics for Decision Making
Week 7 Discussion
Regression
In these discussions, exploration is encouraged!
Each week you must post 3 times (details below):
(Required) Create and post a response that fully answers one of the 10 questions below (no later than Wednesday)
(Required) Create and post a response that fully answers a different one of the 10 questions below (on a different day)
(Required) Post one quality response to another classmates' "main" post or to a professor post (by the end of the week).
(Required) The posts must be submitted on at least 3 different days.
(Optional) Additional posts and/or days of participation are not required, but are certainly welcome!
NOTE: Always paste the question itself (and its number) above your answer (or enough of it, when it's a really long question, to make it clear which one you are addressing).
For full posting guidelines, review the Real World Discussions: Requirements page.
1. Examples - Simple and Multiple Regressions
1. Describe the difference between a simple and a multiple regression. Then include an example of each from your own experiences.
2. Determine the Regression Equation...
2. Determine the regression equation using values you create for x and y for at least 10 pairs of data. Show the regression equation, correlation coefficient, and coefficient of determination. Then switch the x and y values for each data point. Based on that, again show the regression equation, correlation coefficient, and coefficient of determination. Discuss the similarities and differences between the results.
3. Causation versus Relationship
3. Describe the difference between causation between two variables and a relationship between two variables.
4. Hat, No Hat?
4. Explain the difference between y and ?.
5. Week 8 Preparation Question 1
5. If a teacher wanted to compare the shoe size of their 4th grade students with the heights of those same students, which type of graph do you think would be most effective and why?
6. Week 8 Preparation Question 2
6. What graphic depiction would most effectively help a researcher compare the distribution of the hours spent online among teenagers, young adults, and the elderly and why?
7. Week 8 Preparation Question 3
7. Of the statistical processes we have covered throughout this course, which would be most helpful to determine if study hours and sleep could help estimate a student’s test score?
8. Week 8 Preparation Question 4
8. Which statistical method would be most effective to determine if the average size of dogs in Europe was different than the average size of dogs in the U.S.? Why?
9. Week 8 Preparation Question 5
9. A grocery store is looking to purchase new carts for customers to use as they shop. Assuming the amounts purchased are normally distributed, what statistical method would help the store estimate the most likely range of purchases? Why?
10. Ethics! (Strong, not strong?)
10. Ethics: If the computer gives you the slope and intercept for a regression equation, does that mean that the two variables have a strong relationship? Why or why not?
