Medicare/Medicaid Blue Cross/Blue Shield Universal Health 64 69 96 22 64 55 59 68 65 85 48 50 34 48 37 87 27 48 70 84 43 45 107 63 72 63 39 67 59 89 75 73 28 94 4 33 54 91 65 85 59 89 78 54 95 58 87 77 75 60 49 66 78 46 57 42 77 85 53 76 24 83 69 47 51 57 71 72 20 60 59 58 64 76 85 50 74 77 57 41 59 66 20 41 80 91 92 50 56 54 33 20 57 49 77 29 44 42 42 29 72 80 48 70 66 60 56 63 57 35 54 50 82 49 40 31 71 72 30 82 60 50 45 59 64 45 66 64 85 66 65 88 91 52 44 49 19 76 98 83 56 61 47 74 61 8 69 Patriot Insurance 58 41 109 76 105 95 132 88 46 51 97 98 106 77 95 104 76 119 107 74 94 83 89 101 97 85 82 66 76 116 100 98 99 110 104 38 92 111 97 100 104 78 81 69 77 62 72 63 87 76 87 70 75 57 33 66 53 75 60 47 45 64 56 81 61 35 58 70 83 55 96 66 41 56 57 24 50 52 100 79 67 41 65 85 41 68 98 49 62 49 72 64 32 57 90 53 72 31 65 23 73 52 39 80 77 26 62 86 82 60 55 91 55 50 65 34 42 99 48 60 66 31 96 42 62 59 75 71 53 89 67 27 91 84 37 112 56 40 71 16 41 39 57 49 40 53 79 51 48 55 62 64 84 31 64 59 41 46 56 66 51 63 59 90 9 63 36 31 87 89 51 48 88 89 43 42 64 91 69 48 59 66 84 65 96 47 76 34 77 75 76 70 51 79 43 54 71 39 43 101 67 70 126 102 103 73 91 84 65 73 98 94 77 123 83 84 105 84 72 88 65 93 89 67 66 104 111 74 87 108 81 70 109 93 41 60 88 100 97 76 114 106 111 100 89 72 118 103 82 38 64 63 78 Homework Memo 5 Assignment More than Two Samples Significance Testing Instructions Excel Data file name: \"More than Two Samples Test HW5 Memo Data\" Instructions: Follow the HW memo format as noted in the sample assignment. Use a question number heading for each response. Respond with no more than two pages, readable font 12 points, and submit in Word only. Question 1 Situation: The new accounting manager for Briarcliffe Hospital wants to discover if there is a difference in the typical number of days an insured patient stays in the hospital by insurance carrier. The data cover the last year and there are four insurance carriers: Medicare/Medicaid, Blue Cross/Blue Shield, Universal Health, and Patriot Insurance. The analysis requires two variables: A grouping variable (Medicare/Medicaid = 1, Blue Cross/Blue Shield = 2, Universal Health = 3, and Patriot Insurance = 4) and a dependent variable (hospital stay in days). First, determine whether the \"hospital stay in days\" by \"insurance carrier\" data are normally distributed by running descriptive statistics. Second, to discover whether the data has equality of variance, run the Levene test. Last, run a multiple sample test- ANOVA test and, if necessary, the Tukey-Kramer post hoc test. Alpha is .05. Are the data normally distributed? Is there equality of variance? Do hospital stay durations vary by insurance carrier? If so, where specifically are the differences? Report and interpret (explain) your results including the skewness and kurtosis statistics; Levene test; means (ANOVA) and p-values; where appropriate, standard deviations; Tukey-Kramer test, if appropriate; and sample size(s) (60% of assignment points). Question 2 Situation: In this analysis, we have a sample size of 200 students. We wish to determine if there is a relationship between undergraduate college major and intention to attend graduate school. The independent variable consists of the following categories of majors: Healthcare, Math/Science, Engineering, Business, and Education. The dependent variable is comprised of intention to attend graduate school, no intention to attend graduate school, and undecided. The table below provide the frequencies for each category by category (40% of assigned points). Interest in Graduate School by College Major Category Intent to Go to Graduate School Healthcare Math/Science Engineering Business Education Total No Intention Undecided Intends to Go Total 9 11 11 31 9 10 11 30 18 16 8 42 17 11 16 44 17 19 17 53 70 67 63 200 N = 200. Run a multiple sample chi-square test. Is there an overall difference in graduate school intentionality by major? Alpha = .05. Report and interpret your results including frequencies, percentages (proportions), p-value, and whether there is the required minimum 5 count per cell. Question 1 i. The descriptive statistics for hospital stay in days per insurance The data for each variable are not normally distributed. This is because for normal distribution, the mean=mode=median and the coefficient of skewness is zero. In our case, the mean, mode and median are different and the coefficients of skewness for each variable is less than or greater than 0. The output of Levine test is as shown below The p<0.05. thus we reject the null hypothesis for equal variances. Question 2 H0: there is no overall difference in graduate school intentionality by major Ha: there is overall difference in graduate school intentionality by major intention No inten(O) No intent(E) (O-E)2/E healthcare 9 Math/scie 9 engi 18 (O-E)2/E total educ 17 (70*31)/200 (70*30)/200 (70*42)/200 =10.85 =10.50 =14.70 2 2 ( 910.85 ) ( 910.50 ) ( 1814.70 )2 = = 10.85 10.50 14.70 (70*44)/200 (70*53)/200 =15.40 =18.55 2 ( 1715 . 40 ) ( 1718 . 55 )2 15. 40 18. 5 5 0.315438 11 =0.166234 11 =0.129515 19 (67*44)/200 =14.74 ( 1114 . 74 )2 14.74 (67*53)/200 =17.755 ( 1917.755 )2 17.755 0.214286 10 =0.740816 16 Undecided (O) Undecided( (67*31)/200 (67*30)/200 (67*42)/200 E) =10.385 =10.05 =14.07 2 2 2 (O-E) /E ( 1110. 3 85 ) ( 1010.0 5 ) ( 1614.07 )2 10. 3 85 10.05 14.07 Intends (O) Intends (E) business 17 total 70 67 =0.03642 11 (63*31)/200 =9.765 ( 119 . 765 )2 9.765 =0.000249 11 (63*30)/200 =9.45 ( 119 . 4 5 )2 9.45 =0.264741 8 (63*42)/200 =13.23 ( 813 . 23 )2 13.23 =0.948955 16 (63*44)/200 =13.86 ( 1613.86 )2 13.86 =0.087301 17 63 (63*53)/200 =16.695 ( 1716 . 695 )2 16.695 =0.156193 31 =0.254233 30 =2.067491 42 =0.330418 44 =0.005572 53 The test statistic is = ( OE ) E 2 = 5.717862. Using online chi-square calculator available at we find the p-value to be 0.678802 which is greater than 0.05. Therefore, we do not reject the null hypothesis. There is enough evidence to support the claim that there is no overall difference in graduate school intentionality by major. 200