Question

In a survey of smokers who tried to quit smoking with the nicotine patch therapy, 39 were smoking one year after treatment and 32 were not smoking one year after treatment. We want to use a 0.05 significance level to test the claim that among smokers who try to quit with nicotine patch therapy the majority are smoking one year after treatment..

What is the p-value if the claim is modified to state that if the proportion is equal to 0.05?

Answer 1

p : Proportion of smokers who try to quit with nicotine patch therapy are smoking one year after the treatment

Claim :  among smokers who try to quit with nicotine patch therapy the majority are smoking one year after treatment i.e p>0.5

Null hypothesis : p =0.5

Alternate hypothesis : p >0.5 (Right tailed test)

Given,

Number of smokers who try to quit with nicotine patch therapy = 39+32 = 71

Number of smokers were smoking one year of those smokers who try to quit with nicotine patch therapy = 39

Sample proportion smokers who try to quit with nicotine patch therapy are smoking one year after the treatment :

= 39/71=0.5493

For right tailed test :

As P-Value i.e. is greater than Level of significance i.e (P-value:0.203 > 0.05:Level of significance); Fail to Reject Null Hypothesis
There is not sufficient evidence to conclude that among smokers who try to quit with nicotine patch therapy, the majority are smoking one year after treatment

the p-value if the claim is modified to state that if the proportion is equal to 0.05 (i think it's 0.5)

This claim will go in as part of the null hypothesis as null hypothesis will always be '='.Hence

Null hypothesis : p = 0.5

Alternate hypothesis : p0.5 Two tailed test;

For two tailed test ,

Value of the test statistic remains the same,

As P-Value i.e. is greater than Level of significance i.e (P-value:0.406 > 0.05:Level of significance); Fail to Reject Null Hypothesis

There is not sufficient evidence that proportion is not equal to 0.05