You are conducting a project for RDA examining whether stress levels change depending on what participants listen to while studying material. You randomly assign half your participants to listen to white noise while studying material for a test, while the other half listen to nature sounds while studying the material for a test. After $30$ minutes of study, you have each participant complete a $10\u2013$item stress inventory where scores range from $10$ to $50,$ with higher scores meaning higher stress. Specifically, you want to test the hypothesis that the mean stress scores will differ between the two listening groups. The scores for each participant in each group are listed below.

White noise

$31$

$39$

$20$

$37$

$30$

$22$

$27$

$33$

Nature sounds

$32$

$30$

$13$

$23$

$24$

$20$

$15$

$26$

A$.$ Use RStudio to calculate the mean for each group. Report these means.

B$.$ Use RStudio to calculate the standard deviation for each group. Report these SDs$.$

C$.$ Use RStudio to calculate the appropriate t$\u2013$test. Assume that you are testing the hypothesis that is specifically described above.

D$.$ Report the t$\u2013$value obtained. Was it statistically significant? Report the p value obtained to provide support for your answer.

E$.$ Now assume you had predicted that the white noise group would have a larger mean stress score than the nature sounds group. Use RStudio to calculate the appropriate t$\u2013$test under these conditions.

F$.$ Report the t$\u2013$value obtained. Was it statistically significant? Provide the p value obtained to provide support for your answer.

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