Question

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 405 patients who received the antidepressant drug, 39 were not smoking one year later. Of the 395 patients who received the placebo, 50 were not smoking one year later. Given the null hypothesis H0:(pdrug−pplacebo)=0 and the alternative hypothesis Ha:(pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.05,

(a) The test statistic is

(b) The P-value is

Answer 1

Here we have given that,

Claim: To check whether there is difference in two population proportions (Pdrug - Pplacebo) .

The Hypotheses is

v/s

we have given that,

n1= number of patients who received the antidepressant drug =405

x1=number of patients not smoking one year letter=39

The sample proportion is as follows,

1=1^st sample proportion =

n2=number of patients who receivied the placebo =395

X2=number of patients not smoking one year leter= 50

The sample proportion is as follows,

= 2^nd sample proportion =

= level of significance= 0.05

(A)

Now, we can find the test statistics

  

= -1.33

we get

Test statistics= -1.33

(B)

Now, we find the P-value

Pvalue = 2*P( Z < -1.33)

              = 2* (P (Z < -1.33))

              = 2 * ( 0.0918)) USING STANDARD NORMAL Z TABLE

=0.1836

WE GET

P-value = 0.1836

Decision:

Here Pvalue> 0.05

here we fail to reject the Null Hypothesis

Conclusion:

That is here there is Not sufficient evidence that there is the difference in two population proportions.