DA1 Problem 3: Construct a 95% confidence interval estimating the difference between means for both problem 1 and problem 2 and interpret each confidence interval. Comparing the two confidence intervals, what do you notice?This problem is one of four problems in the data analysis assignment. It cannot be answered without the answers to Problems one and two. I am not able to upload a CSV/Excel file, it doesn't allow me to do so. I have included screenshots of the Data Needed to solve Problems one and two, which are needed to solve Problem three. I also included a screenshot of problems one and two to make sure you're able to answer those as well. I only want assistance with Problem 3.Please don't reject my request, I have given all the data necessary to help with answering the question. Lean Mass (DA 1 - Problem 1)StatCrunch Applets EditPlaceboRow1234525678910111213141516171819202122.Supplement5.395.13.894.943.534.978.568.213.536.836.072.614.035.216.392.792.399.392.463.124.350.616.143.952.275.462.273.733.631.713.375.2281.915.086.068.48-0.395.426.04Lean Mass (DA 1 - Problem 2)Dat StatCrunch Applets Edit Data Stat▾ GraphsExperiencepExperienceRow12WN3450678910111213141516171819202122Supplement2.394.033.892.793.124.972.462.616.395.394.948.213.536.073.538.565.216.835.19.39403835343230282624212017151411108532Placebo5.221.911.713.633.732.273.952.274.355.086.0680.61-0.395.463.378.486.045.426.14403736333129275352524221917151312107541H Problem 1: Supplement for WeightliftingImagine you are a statistical consultant and your client, a weightlifting supplement company, islooking 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 20to take a placebo. You have both groups run the same controlled training program over 12 weeksand calculated their whole body lean mass difference in pounds from the beginning to the end ofthe program. Can you infer that the supplement group gained more muscle mass on average thanthe placebo group? Use α=0.05 for any hypothesis test.2a) State the research question in one sentence.a. Do female weightlifters in the supplement group who receive the supplement over12 weeks gain more muscle mass, on average, than those in the placebo groupwho 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 betweenthe average whole body lean mass difference (pounds) from beginning to end ofthe 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. Writeone or two sentences to describe each distribution.Conduct a full F-test to check the equality of the variances (you can assume thepopulations are normal so you can conduct this test). State the hypotheses, calculate thetest statistic, make a decision, and draw a conclusion. You may use technology tocomplete the work.g) Comment on additional methods or strategies to consider when checking if the twopopulation variances are equal.h) Using your work in parts (d) - (g), list all the conditions necessary to complete theoriginal 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 theexact probability).1)Make a decision whether or not to reject or not reject the null hypothesis using both therejection region and the p-value.m) Draw a conclusion by answering the research question.Problem 2 is on the next page.Problem 2: Supplement for Weightlifting ContinuedIn comparison to the previous problem, let us say that the weightlifting supplement companyinformed you that how long a female weightlifter has been lifting impacts the amount of musclemass they can gain. Suppose that you changed your data collection method from what you did inProblem 1. Now you randomly select one weightlifter from each group (supplement andplacebo) that have been lifting for 39 to 40 months. Next, you randomly sample one weightlifterfrom each group that have been lifting for 37 to 38 months. Then, you continue this process untilthe 20th pair of weightlifters have lifted for 2 months or less. The data contains the whole hodylean mass difference in pounds and training experience in months. Can you infer that thesupplement group gained more muscle mass on average than the placebo group? Use α = 0.05for any hypothesis test.a) State the research question in one sentence.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.c) State the correct hypotheses for this question.d) Provide a QQ Plot and a box plot of the differences.e) Comment on the shape of the distribution and determine if outliers are present.f) List the conditions necessary to complete this problem.g) Calculate the test statistic (you may use technology).h) Construct a Rejection Region graph in StatCrunch.i) Calculate the P-value using technology (write the probability statement as well as theexact probability).3i) Make a decision whether or not to reject or not reject the null hypothesis using both therejection region and the p-value.k) Draw a conclusion by answering the research question being posed.1) Comment on the difference in your results from problems 1 and 2. What do you notice?Problem 3: Confidence IntervalsConstruct a 95% confidence interval estimating the difference between means for both problem 1and problem 2 and interpret each confidence interval. Comparing the two confidence intervals,what do you notice?Problem 4 is on the next page.

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DA1 Problem 3: Construct a 95% confidence interval estimating the difference between means for both problem 1 and problem 2 and interpret each confidence interval. Comparing the two confidence intervals, what do you notice?

This problem is one of four problems in the data analysis assignment. It cannot be answered without the answers to Problems one and two. I am not able to upload a CSV/Excel file, it doesn't allow me to do so. I have included screenshots of the Data Needed to solve Problems one and two, which are needed to solve Problem three. I also included a screenshot of problems one and two to make sure you're able to answer those as well. I only want assistance with Problem 3.

Please don't reject my request, I have given all the data necessary to help with answering the question.

Lean Mass (DA 1 - Problem 1)
StatCrunch Applets Edit
Placebo
Row
1
2345
2
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22.
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
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
Lean Mass (DA 1 - Problem 2)
Dat StatCrunch Applets Edit Data Stat▾ Graph
sExperience
pExperience
Row
1
2
WN
3
4
5067
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Supplement
2.39
4.03
3.89
2.79
3.12
4.97
2.46
2.61
6.39
5.39
4.94
8.21
3.53
6.07
3.53
8.56
5.21
6.83
5.1
9.39
40
38
35
34
32
30
28
26
24
21
20
17
15
14
11
10
8
5
3
2
Placebo
5.22
1.91
1.71
3.63
3.73
2.27
3.95
2.27
4.35
5.08
6.06
8
0.61
-0.39
5.46
3.37
8.48
6.04
5.42
6.14
40
37
36
33
31
29
27
535
25
24
22
19
17
15
13
12
10
7
5
4
1
H

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 α=0.05 for any hypothesis test.
2
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.
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.
Problem 2 is on the next page.
Problem 2: Supplement for Weightlifting Continued
In comparison to the previous problem, let us say that the weightlifting supplement company
informed you that how long a female weightlifter has been lifting impacts the amount of muscle
mass they can gain. Suppose that you changed your data collection method from what you did in
Problem 1. Now you randomly select one weightlifter from each group (supplement and
placebo) that have been lifting for 39 to 40 months. Next, you randomly sample one weightlifter
from each group that have been lifting for 37 to 38 months. Then, you continue this process until
the 20th pair of weightlifters have lifted for 2 months or less. The data contains the whole hody
lean mass difference in pounds and training experience in months. Can you infer that the
supplement group gained more muscle mass on average than the placebo group? Use α = 0.05
for any hypothesis test.
a) State the research question in one sentence.
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.
c) State the correct hypotheses for this question.
d) Provide a QQ Plot and a box plot of the differences.
e) Comment on the shape of the distribution and determine if outliers are present.
f) List the conditions necessary to complete this problem.
g) Calculate the test statistic (you may use technology).
h) Construct a Rejection Region graph in StatCrunch.
i) Calculate the P-value using technology (write the probability statement as well as the
exact probability).
3
i) Make a decision whether or not to reject or not reject the null hypothesis using both the
rejection region and the p-value.
k) Draw a conclusion by answering the research question being posed.
1) Comment on the difference in your results from problems 1 and 2. What do you notice?
Problem 3: Confidence Intervals
Construct a 95% confidence interval estimating the difference between means for both problem 1
and problem 2 and interpret each confidence interval. Comparing the two confidence intervals,
what do you notice?
Problem 4 is on the next page.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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