Please explain how you solve this problem (please explain in detail) Also, can y

Question

Please explain how you solve this problem (please explain in detail)

Also, can you explain how I have to solve the problem if "smokers in men is less than that in women" change to "smokers in men is greater than that in women" ?

There are 150 smokers in a random sample of 500 women, whereas 110 smokers are found in a random sample of 500 men. Let p, and p2 be the proportion of smokers in women and men respectively. At significance level 0.002, are the samples showing strong evidence that proportion of smokers in men is less than that in women? OYES ONO Note: Use 4 decimal places for Pi. P2, and 2 decimal places for z-score of dp

Explanation / Answer

Sol:

let p1=proportion of women

p2=proportion of men

Hypotheses are:

H0:p1=p2

men less than women implies women greater than men

H1:p1>p2

alpha=0.002

conf.level=1-alpha=1-0.002=0.998

p1^=sample prop of women=150/500=0.3

p2^=sample prop of men=110/500=0.22

p bar=x1+x2/n1+n2=15+110/500+500=0.26

Z=p1^-p^/sqrt(p bar*(1-pbar)(1/n1+1/n2)

=0.3-0.22/sqrt(0.26(1-0.2)(1/500+1/500)

=2.884

Z=2.88
Z crit=2.88

Z >Z crit

p=0.002

p<0.002

Reject Null hypothesis.

Accept alternative Hypothesis.

ANSWER:YES

Reject Null hypothesis

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