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A sleep center hypothesizes that people who sleep only four hours will score lower than people who sleep for eight hours on a cognitive skills test.
Group Y: Four hrs sleep
Conduct the following hypothesis test:
- A one-tail T-test for a two-sample difference in means at the 95% confidence level
- with Null Hypothesis that the Group X mean CAT score is equal to the Group Y mean CAT score
- and with Alternate Hypothesis that the Group X mean CAT score is greater than the Group Y mean CAT score
1. Calculate the mean and standard deviation of the scores for each group. (10%)
2. Using the correct degrees of freedom (df = group X size + group Y size ̶ # of groups), the correct number of tails, and at the correct confidence level, determine the critical value of t. (10%)
3. Explain under which scenarios using a pooled variance be inadvisable, then, calculate the pooled variance (formula for S2 is onpage 379) for the groups. (10%)
4. Calculate the test statistic, Ttest (formula for t is on page 380). (10%)
5. The sleep center's statistician tells you that the p-value for the test is 0.1535. Summarize the result of the study. Compare the mean scores in each group. Compare the test statistic to the critical value. Compare the p-value to alpha. Do you find a statistically significant difference between Group X and Group Y on cognitive test performance? Is there a meaningful/practical difference? Explain your decisions and Justify your claims. (15%)
