statistics
vaniac
Exam1.docxPSYC 2317 Take Home Test #1
Barry is currently obese and would like to lose weight. Barry is watching television and sees two different infomercials about weight loss products. The first infomercial is for a weight loss “supplement”, called ICBINM (I Can’t Believe It’s Not Meth), the customer takes daily to “increase metabolism and energy”. The infomercial for ICBINM shows 3 different verified customers who used the product and lost a lot of weight. The second infomercial is for a weight loss “program”, called TNKD (The North Korean Diet), which tightly regulates which foods you eat and briefly “re-educates” (i.e., tortures) customers who break any diet rules, to reinforce the importance of sticking to the program. The infomercial for TNKD also shows 3 verified customers who followed the program and lost a lot of weight.
Barry is interested in both of these products, but he wants more information before he decides whether to order either product. He calls up both companies and asks for any weight loss data they have for people who have used their product. Both companies indicate they have conducted research in which they had people use their product for 3 months and measured how much weight each person lost. Below is the data each company provides Barry.
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ICBINM: weight loss (in pounds) for 25 customers who used the product for 3 months |
TNKD: weight loss (in pounds) for 25 customers who followed the diet plan for 3 months |
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1) (5 points) What scale of measurement is the weight loss data (shown above) on? If you wanted to measure weight loss on a nominal scale of measurement, how would you do that? If you wanted to measure weight loss on an ordinal scale of measurement, how would you do that?
2) (15 points) Calculate the following information for each of the data sets given above: mean, median, standard deviation, minimum score, maximum score, 25th percentile score, 75th percentile score, interquartile range. Write a description of these two data sets based on your calculations. What do the mean and standard deviation tell you about the effectiveness of ICBINM and TNKD?
3) (5 points) Provide a group frequency distribution of each data set given above.
4) (5 points) Provide a histogram of the ICBINM data
5) (5 points) Provide a frequency polygon of the TNKD data.
6) (5 points) Create a box plot for each of the data sets.
7) (10 points) Would it be a better idea to use the median, rather than the mean, to summarize either (or both) of these data sets? Explain why or why not.
8) (10 points) If Barry decides he is definitely going to purchase one of these two products to help him lose weight. Based on your analysis of the data for ICBINM and TNKD, which product is Barry better of using? Explain why you chose that product for Barry.
9) (10 points) Timmy and Fred are both 5th grade students taking geography. Timmy is in Mr. Beard’s class and Fred is in Mr. Donovan’s class. Both Timmy and Fred just took their first geography test in their respective classes, and are comparing their scores to figure out who is the better student. Timmy earned an 87 (out of 100) on his test; whereas, Fred earned an 83 (out of 100) on his test. Timmy brags that he is clearly the better student because he earned a higher test score. Fred disagrees and points out that they not only have different teachers, but also took somewhat different tests. Fred argues that you can’t just directly compare their test scores because maybe Mr. Beard is a better teacher, or Timmy’s test was easier than Fred’s test. Using the data given below, perform the necessary statistical calculations to help Timmy and Fred figure out who is the better student based on their test scores.
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Beard’s Class |
Donovan’s Class |
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Mean Test Score () |
83.35 |
80.59 |
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Standard Deviation (s) |
7.42 |
4.11 |
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# of Students |
36 |
46 |
10) 5 EXTRA POINT QUESTION
If the ICBINM commercial featured 3 customers who lost 82, 85, and 90 pounds after using the product for 3 months; is this method of advertising misleading in any way? Explain why it is, or is not, misleading using the data provided in the data set above. NOTE: You must present statistical calculations to back up your claim that the advertising is/is not misleading (HINT: this involves outliers which we did not have time to discuss).
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