Question

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 a completely different and unrelated five students and give them the same lesson on a rainy day. These are their results for a quiz on their lesson:

Sunny Day Students:

• Student 1: 9.8
• Student 2: 6.7
• Student 3: 7.2
• Student 4: 8.2
• Student 5: 5.1

xbar₁ = 7.4

Rainy Day Students:

• Student 6: 8.2
• Student 7: 6.7
• Student 8: 6.8
• Student 9: 9.7
• Student 10: 7.1

xbar₂ = 7.7

a. State the null and alternative hypotheses.

b. What are the degrees of freedom for this t-test? Find the corresponding critical t-value(s) for Type I error rate (alpha) of α = 0.05?

c. Calculate your observed t-statistic (hint: you will need to calculate the standard deviations of both groups first).

d. Compare your observed t-statistic to the critical t-value. 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).

Answer 1

e) Interpretation of confidence interval - About 95 out of 100 situations our sample mean will lie in this interval.

f) Interpretation of Effect size - Cohen's d =0.2769

Which means that effect size is small as it is less than 0.3. PL??