Amatuer and professional singers were the subjects of a study. The researchers i

Question

Amatuer and professional singers were the subjects of a study. The researchers investigated the possible beneficial effects of singing on well-being during a single singing lesson. One of the variables of interest was the change in cortisol as a result of the singing lesson. Use the data to determine if cortisol levels are different before and after a singing lesson.

Based on the assumptions, what type of test should you perform, a paired t-test or a non-parametric Wilcoxon Signed Rank test?

What are the null and alternative hypotheses based on the test you chose in part a?

What is the test statistic and p-value for the test you chose in part a.

What is your conclusion to the test you performed stated in the context of the problem?

Subject 1 2 3 4 5 6 7 8 Before 214 362 202 158 403 219 307 331 After 232 276 224 412 562 203 340 313

Explanation / Answer

Data foloows Normal distribution.we can use here parametric paired t test.

Using Minitab,

Paired T-Test and CI: Before, After

Paired T for Before - After

N Mean StDev SE Mean
Before 8 274.5 87.8 31.0
After 8 320.3 119.6 42.3
Difference 8 -45.8 108.8 38.5

95% CI for mean difference: (-136.7, 45.2)
T-Test of mean difference = 0 (vs not = 0): T-Value = -1.19 P-Value = 0.273

P-value >0.05 we do not reject null hypothesis

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