Please show all work thank you A drug company is testing the

Please show all work, thank you.

A drug company is testing their new drug to help perpetually bored students stay awake in their courses. The company collected a sample of 7 students, subjected them to an incredibly boring 3 hour lecture about statistics, and measured the number of minutes they managed to stay awake. They then administered their new drug to each student, and after doing so, once again subjected them to the same boring 3 hour lecture, measuring the number of minutes they managed to stay awake. The following table gives the before and after results of the new drug: Test whether the after drug increases the number of hours students stay awake using the following tests (using alpha = 0.05 for each test): (a) Paired t test. (b) Sign test. (c) Wilcoxon signed-rank test.

Solution

H0: mu1 = mu2

Ha: mu1 < mu2.

where mu1 = mean hours awake before drug and mu2 = mean hours awake after drug.

Left tailed test.

a) Paired t test.

t = 1.1031
  df = 6
  standard error of difference = 1.554

p value = 0.1561

As p >= 0.05 this difference between means not significant.

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b) Sign test.

Difference is not significant as p >0.05

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c) Wilcoxon signed rank test.

The W-value is 5.5. The critical value of W for N = 6 at p 0.05 is 2. Therefore, the result is not significant at p 0.05.

Group	Group One	Group Two
Mean	22.86	24.57
SD	12.39	12.05
SEM	4.68	4.56
N	7	7