Question

the lengths of time (in years) it took a random sample of 32 former smokers to quit smoking permanently are listed. assume the population standard deviation is 4.3 years. at $\alpha=0.01$, is there enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years? complete parts (a) through (e).
10.7 22.7 17.7 14.4 19.6 21.7 11.8 9.9
18.4 10.7 9.5 9.6 13.3 22.3 15.4 21.4
8.1 14.2 12.6 14.4 11.2 16.3 8.7 19.3
20.8 7.2 18.9 22.4 7.1 9.4 8.3 7.8
(b) identify the standardized test statistic. use technology.
$z = 1.64$ (round to two decimal places as needed.)
(c) find the p - value. use technology.
$p = 0.101$ (round to three decimal places as needed.)
(d) decide whether to reject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim at the 1% level of significance.
a. fail to reject $h_0$. there is not sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.
b. fail to reject $h_0$. there is sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.
c. reject $h_0$. there is not sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.
d. reject $h_0$. there is sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.

Explanation:

Step1: Recall the decision rule for hypothesis testing

Compare the P - value with the significance level \(\alpha\). If \(P\leq\alpha\), reject \(H_0\); if \(P > \alpha\), fail to reject \(H_0\).

Step2: Compare the P - value and \(\alpha\)

Given \(\alpha = 0.01\) and \(P=0.101\). Since \(0.101>0.01\) (i.e., \(P > \alpha\)).

Answer:

A. Fail to reject \(H_0\). There is not sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.