Question

3. As a medical social worker in a local hospital, you are asked to evaluate the success of a group instruction diabetic control program. You randomly assign twelve diabetic patients to the group program and twelve to the more traditional personal instruction program. Over a twelve-month period you collect data on the number of hospital admissions and emergency room visits for uncontrolled blood sugar for individuals in each group. These data are presented below. You are to analyze these data using an independent-samples test and then make a recommendation to the medical director as to whether to continue the program (Set ce=05). (15 points) Number of admissions and emergency room visits Group Instruction Personal Instruction n-12 X-1.4 S-1.2 n2-12 X-2.3 S-12

Answer 1

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: μι > μ2 Ha: 2 This corresponds to a left-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. (2) Rejection Region Based on the information provided, the significance level is a 0.05, and the degrees of freedom are df 22. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal: Hence, it is found that the critical value for this left-tailed test is te = -1.717, for a = 0.05 and df 22 The rejection region for this left-tailed test is R {t: t -1.717}. (3) Test Statistics Since it is assumed that the population variances are equal, the t-statistic is computed as follows: X2 (n1-1)s+(n2-1) s n1+n2-2 n2 1.4 2.3 -1.837 (12-1)1.22 +(12-1)1.22 12+12-2 + (4) Decision about the null hypothesis -1.717 , it is then concluded that the null hypothesis is -1.837<te Since it is observed that t rejected.

We conclude that the null hypothesis is rejected

hence there is evidence that mean for group instruction is less.

we should continue the program