STAT 130 Fall 2018 Case Study Wentworth Medical Center As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth Medical Center in upstate New York investigated the relationship between geographic location, gender and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression. The data collected follow; higher test scores indicate higher levels of depression. You should consider the following instructions when answering the case study questions and preparing your report: I. For confidence intervals: ➢ Check all assumptions. ➢ Interpret the results. II. ➢ ➢ ➢ ➢ III. For testing hypothesis: State the null and alternative hypotheses. Check the necessary assumptions. Report the P-value and the test statistic. Make a conclusion statement in the words of the original problem. For the report ➢ ➢ ➢ ➢ ➢ Should be typed. On the first page, write the names, student numbers, and section number. All pages must be stapled together. Show all of your work. The report should have the following item: ❖ ❖ ❖ ❖ ❖ ❖ ❖ Title Table of Contents Executive Summary Introduction Main text Conclusions Recommendations STAT 130 Fall 2018 Case Study Case Study Questions: answer all the following questions and write your report. a) Use descriptive statistics to summarize the data. b) Develop a 95% confidence interval estimate of the mean depression value for the 60 individuals. c) Develop a 95% confidence interval estimate of the mean depression value for residents of Florida. d) Is the mean of depression value for the 60 individuals different than 5.5? Use a 0.05 level of significance (test the hypotheses using both p-value and C.I method). e) Is there any significant difference of the mean of depression value due to gender? Use a 0.05 level of significance. f) Develop a 95% confidence interval estimate of the mean of depression value difference for male and female. g) Explain how your conclusion in part e can be derived from part f. h) Is there any significant difference of the mean of depression value due to geographic location? Use a 0.05 level of significance. i) Give point estimates for the proportion of individuals according to their gender. j) Is there a difference in the proportions of female between New York and North Carolina states? Use a 0.05 level of significance. k) Develop a 95% confidence interval of the difference in proportion of male between New York and North Carolina states. STAT 130 Fall 2018 Case Study l) Is the depression in gender affect by the Geographic locations? Use a 0.05 level of significance. m) locations Number of depressed persons Florida New York North Carolina 23 17 20 Is the distribution of the depressed peoples across locations uniform ( = 33%, = 33%, = 33% )? Use a 0.05 level of significance.