Question

(3 pts) Suppose a group of 700 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 546 patients who received the antidepressant drug, 259 were not smoking one year later of the 154 patients who received the placebo 62 were not smoking one year later. Given the null hypothesis IT : (Pr - Parte) and the alternative hypothesis H.: (Pdry - Plote) conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use a = 0.01 (a) The test statistic is (b) The P-value is

Answer 1

Given that From samble Doug Sample size (n.) = 546 Doug Sample Probortion = P. 259 546 Plong Pasug = 0.4744 From Placebo Sample Sample Size (M₂) = 154 Placebo Sample Proportion Pehredo? 62 Isu =) P Placelo = 0.4026 Pooled Sample Proportion P 259 +62 546 + 154 P=0.4586 cs Scanned with CamScanner

Null hypothesis (Ho) Pdsug - Pplacebo = 0 Alternative hypothesis (Ha) : Pasug - Poplacebo to test, This corresponds to for which Zatest is used, a two-tailed two Population Proportions a Critical Value Given d20.01 bor two-tailed last the Z Grilical value Zc - 2:58 ic, > 2.58 Rejech Ho it lzl Test Statistic The Z - statistic is computed as follows Parung -Po Placebo 근 N(0,0) P(1-P) (ht 0.4744 0.4026 0.4586 0.5414 Swot tsu CS Scanned with CamScanner

0.0718 근 1 0.0021 0718 0.0458 Z = 1.57 ca) The testi statistic is Z-1.57 (6) P-value The P-value p is P= P(171> 1.57) P(Z < -1.57) + P(Z > 1.57) 0.058 + 0 P O. 116 0.116 ". The P-value وبيا 0.0lad Pa 0.116 observe that the null It is concluded that hypothesis not rejected ( fail to reject fail to reject Ho) cs Scanned with CamScanner

The test statistic value is z= 1.57

The p value is p=0.116