Question

Suppose a group of 1000 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 120 patients who received the antidepressant drug, 32 were not smoking one year later. Of the 880 patients who received the placebo, 50 were not smoking one year later. Given the null hypothesis H0:(pdrug−pplacebo)=0H0:(pdrug−pplacebo)=0 and the alternative hypothesis Ha:(pdrug−pplacebo)≠0Ha:(pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.01α=0.01,

(a) The test statistic is

(b) The P-value is

(c) The final conclusion is

A. There seems to be evidence that the patients taking the antidepressant drug have a different success rate of not smoking after one year than the placebo group.
B. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.

please show your work and what function , f any you use on the calulator. Thank you !

Answer 1

using excel>addin.phstat>two sample test >2 proportion

we have

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.01
Group 1
Number of Items of Interest	32
Sample Size	120
Group 2
Number of Items of Interest	50
Sample Size	880
Intermediate Calculations
Group 1 Proportion	0.266666667
Group 2 Proportion	0.056818182
Difference in Two Proportions	0.209848485
Average Proportion	0.0820
Z Test Statistic	7.8598
Two-Tail Test
Lower Critical Value	-2.5758
Upper Critical Value	2.5758
p-Value	0.0000
Reject the null hypothesis

Suppose a group of 1000 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 120 patients who received the antidepressant drug, 32 were not smoking one year later. Of the 880 patients who received the placebo, 50 were not smoking one year later.

the null hypothesis H0:(pdrug−pplacebo)=0

the alternative hypothesis Ha:(pdrug−pplacebo)≠

α=0.01,

(a) The test statistic is 7.8598

(b) The P-value is 0.0000

(c) The final conclusion is

A. There seems to be evidence that the patients taking the antidepressant drug have a different success rate of not smoking after one year than the placebo group.