8. Finally, we consider some potential psychological aspects of the coronavirus situation, by considering a past study. In the study, a large random sample of subjects was rated on their overall degree of social connection to others (categorized as strong, moderate, or weak) and then they were given a psychological questionnaire that rated their happiness (categorized as very happy, somewhat happy, or not happy). The results are tabulated as follows: SOCIAL CONNECTION Strong Moderate Weak Very 1748 418 62 2228 HAPPINESS Somewhat 2804 1038 115 3957 Not 580 188 24 792 5132 1644 201 6977 Here is some EDA from the study: Bar Graph of Happiness, given Social Connection (out of each social connection category) percent very happy not happy very happy not happy very happy not happ moderately happy moderately happy moderately happy Strong Moderate Weak 8 (a) In order to check that you understand the display, please use the data to compute the actual proportion represented by the height of the leftmost dark-shaded bar. Show calculation. [3 pts ] [exercise 8 continues on the next two pages]8 (b) For the 'cxereise 8' scenario from the previous page, state the appropriate formal Null and Alternative Hypotheses. [4 p15] Software produced the following expected counts corresponding to each cell of the table (note that one value has been blanked-out]: Expected Counts: strong moderate very - 524 . 99 somewhat 2910.61 582.56 8 (c) Compute the expected count of strong-socially-connected and very-happy that is blanked-out in the above soware output, by applying the appropriate expected count formula. [Show work] [2 pa] Software also produced the following chi square contributions corresponding to each cell of the table (note that one values has been blanked-out]: Chi square contributions: Strong moderate very - 21.803 somewhat 11 . 961 8 (d) Use the appropriate formula to compute the chisquare contribution (blanked-out in the previous output) corresponding to the 'strongsociallyconnected and very- happy' cell in the table. Please show your calculation. [2 pts] [exercise 8 continues on the next page] Software also produced the following for the formal chi square test corresponding to the 'exercise 8' scenario: Chi-Square = 45.108 P-Valuo = 0 8 (e) State the formal conclusion to the signicance test (regarding whether or not you reject the null hypothesis), with brief explanation of how you are making your conclusion. (Use a signicance level of'ODSJ [a put] 8 (0 State the meaning of your previous conclusion in the context of the original story. [3 pm] 8 (3) Based on your conclusion in part (e), are these results statistically significant? Give the letter (P, Q, R, or S) of the best answer: [2 pts] P: Yes. because Statistics was used to make a conclusion. 0: Yes. because the differences in the study were probably not due to random chance. R: No. because the formal result contradicts our commonsense expectation. S: No, because the differences in the study were probably due merely to random chance
