Problem 1: Supplement for Weightlifting Imagine you are a statistical consultant and your client, a weightlifting supplement company, is looking to see if their product is effective in increasing muscle mass gained over a training cycle. You randomly sampled 20 female weightlifters and assigned them to take the supplement and 20 to take a placebo. You have both groups run the same controlled training program over 12 weeks and calculated their whole body lean mass difference in pounds from the beginning to the end of the program. Can you infer that the supplement group gained more muscle mass on average than the placebo group? Use a = 0.05 for any hypothesis test.

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If I could have help with answering Problem one, I would greatly appreciate it. I have the data files in the form of a screenshot. I would have uploaded it as a CSV/Excel file, but I am not able to on this website.

Problem 1: Supplement for Weightlifting
Imagine you are a statistical consultant and your client, a weightlifting supplement company, is
looking to see if their product is effective in increasing muscle mass gained over a training cycle.
You randomly sampled 20 female weightlifters and assigned them to take the supplement and 20
to take a placebo. You have both groups run the same controlled training program over 12 weeks
and calculated their whole body lean mass difference in pounds from the beginning to the end of
the program. Can you infer that the supplement group gained more muscle mass on average than
the placebo group? Use a = 0.05 for any hypothesis test.
a) State the research question in one sentence.
a. Do female weightlifters in the supplement group who receive the supplement over
12 weeks gain more muscle mass, on average, than those in the placebo group
who receive no supplement?
b) Use the question to determine the parameter we are using to conduct statistical inference.
Describe this parameter in one sentence using symbols and a description.
a. The parameter used to conduct the statistical inference is the difference between
the average whole body lean mass difference (pounds) from beginning to end of
the program for the supplement group and the placebo group.
c)
State the correct hypotheses for this question.
d) Provide a QQ Plot and a box plot to analyze the shape of each of the sample distributions.
e) Comment on the shape of the distributions and determine if outliers are present. Write
one or two sentences to describe each distribution.
f)
Conduct a full F-test to check the equality of the variances (you can assume the
populations are normal so you can conduct this test). State the hypotheses, calculate the
test statistic, make a decision, and draw a conclusion. You may use technology to
complete the work.
g) Comment on additional methods or strategies to consider when checking if the two
population variances are equal.
h) Using your work in parts (d) - (g), list all the conditions necessary to complete the
original hypothesis test (the hypothesis test based on the original research question).
Calculate the test statistic of this hypothesis test (you may use technology).
j) Construct a Rejection Region graph in StatCrunch.
i)
k) Calculate the P-value using technology (write the probability statement as well as the
exact probability).
1) Make a decision whether or not to reject or not reject the null hypothesis using both the
rejection region and the p-value.
m) Draw a conclusion by answering the research question.
Transcribed Image Text:Problem 1: Supplement for Weightlifting Imagine you are a statistical consultant and your client, a weightlifting supplement company, is looking to see if their product is effective in increasing muscle mass gained over a training cycle. You randomly sampled 20 female weightlifters and assigned them to take the supplement and 20 to take a placebo. You have both groups run the same controlled training program over 12 weeks and calculated their whole body lean mass difference in pounds from the beginning to the end of the program. Can you infer that the supplement group gained more muscle mass on average than the placebo group? Use a = 0.05 for any hypothesis test. a) State the research question in one sentence. a. Do female weightlifters in the supplement group who receive the supplement over 12 weeks gain more muscle mass, on average, than those in the placebo group who receive no supplement? b) Use the question to determine the parameter we are using to conduct statistical inference. Describe this parameter in one sentence using symbols and a description. a. The parameter used to conduct the statistical inference is the difference between the average whole body lean mass difference (pounds) from beginning to end of the program for the supplement group and the placebo group. c) State the correct hypotheses for this question. d) Provide a QQ Plot and a box plot to analyze the shape of each of the sample distributions. e) Comment on the shape of the distributions and determine if outliers are present. Write one or two sentences to describe each distribution. f) Conduct a full F-test to check the equality of the variances (you can assume the populations are normal so you can conduct this test). State the hypotheses, calculate the test statistic, make a decision, and draw a conclusion. You may use technology to complete the work. g) Comment on additional methods or strategies to consider when checking if the two population variances are equal. h) Using your work in parts (d) - (g), list all the conditions necessary to complete the original hypothesis test (the hypothesis test based on the original research question). Calculate the test statistic of this hypothesis test (you may use technology). j) Construct a Rejection Region graph in StatCrunch. i) k) Calculate the P-value using technology (write the probability statement as well as the exact probability). 1) Make a decision whether or not to reject or not reject the null hypothesis using both the rejection region and the p-value. m) Draw a conclusion by answering the research question.
Row
123456
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Supplement
5.39
5.1
3.89
4.94
3.53
4.97
8.56
8.21
3.53
6.83
6.07
2.61
4.03
5.21
6.39
2.79
2.39
9.39
2.46
3.12
Placebo
4.35
0.61
6.14
3.95
2.27
5.46
2.27
3.73
3.63
1.71
3.37
5.22
8
1.91
5.08
6.06
8.48
-0.39
5.42
6.04
Transcribed Image Text:Row 123456 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Supplement 5.39 5.1 3.89 4.94 3.53 4.97 8.56 8.21 3.53 6.83 6.07 2.61 4.03 5.21 6.39 2.79 2.39 9.39 2.46 3.12 Placebo 4.35 0.61 6.14 3.95 2.27 5.46 2.27 3.73 3.63 1.71 3.37 5.22 8 1.91 5.08 6.06 8.48 -0.39 5.42 6.04
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