Question

For each of the following studies, the samples were given an experimental treatment and the researchers compared their results to the general population (all populations are normally distributed). For each, carry out a Z test using the 5 steps of hypothesis testing for a two-tailed test. Figure the 95% confidence intervals for each study. Be sure your answers for each study include the: SDM, Cut-off Z, Sample Z, Conclusion, and 95% Confidence Interval.

Study Population Sample size Sample mean Significance level M SD N a). 36 8 16 38 .05 b). 36 6 16 38 .05 c). 36 4 16 38 .05 d). 34 4 16 38 .01

Answer 1

(a)Null hypothesis H, : 4 = 36 Alternative hypothesis H: 4736 Let the level of significance be a = 0.05, then the critical values are $20.052 = £1.96. Test statistic Zc 1-4 38-36 = 1.00 ol yn 8/V16 The value of the test statistic Zcu = 1.00, lies between the critical values. It falls in acceptance region. We fail to reject the null hypothesis. = प J 100(1-a)% confidence interval for true (population) mean is 7 – Zw12: ., +Z/2 172 95% confidence interval for population mean is 8 8 38-1.96 ,38+1.96 = (34.08,41.92). Conta V16 (b) Null hypothesis H: 4 = 36 Alternative hypothesis 4:47 36 Let the level of significance be a = 0.05, then the critical values are Zoosa = 1.96. 38-36 Test statistic Zca = 1.33 olin 6/16 The value of the test statistic Z = 1.33, lies between the critical values. It falls in acceptance region. We fail to reject the null hypothesis. - 100(1-a)% confidence interval for true (population) mean is 7 – Zw12: +Z Vn 95% confidence interval for population mean is 6 6 38-1.96 ,38+1.96 ()- = (35.06,40.94)

(Null hypothesis 4 : 4 = 36 Alternative hypothesis H: 4736 Let the level of significance be a = 0.05, then the critical values are $20.052 = £1.96. Test statistic Zc 1-4 38-36 - 2.00 oln 41 V16 The value of the test statistic Z = 2.00, does not lies between the critical values. It falls in rejection region. We reject the null hypothesis. = प प 100(1-a)% confidence interval for true (population) mean is 7 – Zw12: ., 7+26/2 172 () V16 95% confidence interval for population mean is 4 38-1.96 ,38+1.96 = (36.04,39.96) V16 (d) Null hypothesis H, : 4 = 34 Alternative hypothesis H:47 34 Let the level of significance be a = 0.01, then the critical values are $2.012 = +2.58. 1-44 38-34 Test statistic Z : 4.00 olt 4/ 116 The value of the test statistic Zca = 4.00, does not lies between the critical values. It falls in rejection region. We reject the null hypothesis. ह 100(1-a)% confidence interval for true (population) mean is 7 – Zw12: +Z Vn 99% confidence interval for population mean is 4 38-2.58 38+2.58 .) = (35.42,40.58). V16 16