Suppose a group of 800 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 526 patients who received the antidepressant drug, 14 were not smoking one year later. Of the 274 patients who received the placebo, 107 were not smoking one year later. Given the null hypothesis H0 : grim."g — ppgacebo) = 0 and the alternative hypothesis Ha : (mmg — ppgacebo) 75 0, 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 (c) The final conclusion is o 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. O B. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.

(a) -13.6321

(b) < .00001

(c)

B. there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.  

Step-by-step explanation

(a)

Let 

p_x = proportion of patients who received an antidepressant drug who were not smoking one year later 

p_y = proportion of patients who received the placebo who were not  smoking one year later 

Ho: p_x - p_y = 0 vs. Ha: p_x - p_y ≠ 0 with

???? = 0.01 

Test statistic formula: Z=p(1−p)(n1?1?+n2?1?)?(px?−py?)−do??with critical region ?Z?>zα/2?  = ?Z?>z0.01/2?. The critical value is z0.01/2=0.005?= 2.576 

p_x = 52614?,  p_y = 274107? , d_o = difference in the hypothesis which is 0 

p = n1?+n2?X+Y? = 526+27414+107? = 800121?

Plug in the values in the test statistic formula, we have 800121?(1−800121?)(5261?+2741?)?(52614?−274107?)−0?=−13.6321

(b) 

P value, or calculated probability, is the probability of finding the observed, or more extreme, results when the null hypothesis (H₀) of a study question is true. we use a simulation or other technology to find the P-value from the standard normal curve. 

z score is -13.6321 

The P-Value is < .00001.
The result is significant at p < .01.

(c)

Since -13.6321 is not > 2.576, we do not reject Ho. At 1% level of significance, there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year. 

Source

https://www.statsdirect.com/help/basics/p_values.htm