HSCI 2117: Problem Set 5 - Z-Tests and T-Tests Show all work and calculations for all questions on this problem set. If you use excel, attach the excel file to your submission. Include in your final word document a description of the process and method you used to solve each question. Provide sufficient explanation of how you got the answer to any question. The percent of hospitals in Region 3 of the northwestern United States that reached maximum occupancy at least once in 2015 was 78%. The regional administrator wants to conduct a study to determine if the rate has gone down. Before conducting the study, she assumes that the average rate is still 78%. She calls a sample of 200 hospitals in the region and finds that 148 of the 200, or 74%, reached maximum occupancy at least once during 2016. Use this information to answer questions 1-4. Conduct the following hypothesis test: - A one-tail Z-test for a one-sample proportion at the 90% confidence level - with Null Hypothesis that the proportion of hospitals who reach maximum occupancy at least once per January in region is equal to 78% - and with Alternate Hypothesis that the proportion of hospitals who reach maximum occupancy at least once per January in region has gone down and is no longer 78%. 1. 2. 3. 4. Identify the correct critical value, Z. (10%) Calculate the test statistic, Ztest. (10%) Calculate P(Z < Ztest). (10%) Compare the test statistic to the critical value. Compare P(Z< Ztest) to . Compare the sample proportion to the null hypothesis proportion. Is there a statistically significant difference to suggest that the hospital max occupancy rate in 2016 is less that the rate was in 2015? Is there a practically significant difference? (15%) 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. The center recruited 20 participants and split them into two groups, giving one group 8 hours of sleep and the other only 4 hours. The following morning, the CAT (Cognitive Ability Test) was conducted, with scores ranging from 19, 9 being the best score. Use this information to answer questions 5-9. CAT Scores Group X: Eight hrs sleep 4 7 9 4 3 3 8 6 3 7 7 8 1 4 2 3 5 2 7 4 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 5. Calculate the mean and standard deviation of the scores for each group. (10%) 6. 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%) 7. Explain under which scenarios using a pooled variance be inadvisable, then, calculate the pooled variance (formula for S2 is on page 379) for the groups. (10%) 8. Calculate the test statistic, Ttest (formula for t is on page 380). (10%) 9. 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%)