1) It may be that sunshine has a unique effect on learning statistics. Previous research has been in disagreement, with some studies showing that sunshine increases amount learned whereas others show sunshine has detrimental effects on learning. You would like to determine for yourself whether or not sunshine makes a DIFFERENCE on statistics learning. Let's assume you take five statistics students and give them a lesson on a sunny day, and then take the same students and give them the a related lesson on a rainy day. These are their results for a quiz on their lesson:

Sunny Day Results:

• Student 1: 20.8
• Student 2: 17.9
• Student 3: 18.3
• Student 4: 19.2
• Student 5: 16.1

Rainy Day Results:

• Student 1: 19.2
• Student 2: 17.7
• Student 3: 17.8
• Student 4: 20.5
• Student 5: 18.0

a. State the null and alternative hypotheses

b. What are the degrees of freedom for yourttest? Find the corresponding criticalt-value for Type I error rate (alpha) of = 0.05.

c. Calculate your observedt-statistic (hint: you will need to calculate the average difference scores and the SD of the average difference score first).

d. Compare your observedt-statistic to the critical t-value(s). What do you conclude regarding the null hypothesis?

e. Calculate and interpret the 95% Confidence interval.

f.Calculate and interpret the standardized effect size (Cohen's d).

g. What do you conclude about your research question (use your own words, in everyday language).