JustAnswer
The length of time (in years) it took a random sample of 32 former smokers to quit smoking permanently are listed. At alpha = 0.05, is there enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 15 years?
15.7, 13.2, 22.6, 13.0, 10.7, 18.1, 14.7, 7, 17.3, 7.5, 21.8, 12.3, 19.8, 13.8, 16.0, 15.5, 13.1, 20.7, 15.5, 9.8, 11.9, 16.9, 7.0, 19.3, 13.2, 14.6, 20.9, 15.4, 13.3, 11.6, 10.9, 21.6
a. write the claim mathematically
b. find the standardized test statistic z, and its corresponding area
c. find the p value
d. decided to reject or fail the null hypothesis
e. interpret the decision and the context of the original claim
Answer
From the data we compute the following.
Sample size = [pic]
Sample mean = [pic]
Sample standard deviation = [pic] = 4.29
a) Let [pic] denote the mean time it takes a smokers to quit smoking.
Null hypothesis: [pic]
Alternative hypothesis: [pic]
b) The test statistic used is
[pic]
[pic]
c) The p-value is [pic]
d) Since the p-value is not less than the significance level 0.05, we cannot reject the null hypothesis. The evidence in the sample is not enough to reject the claim that the mean time it takes smokers to quit smoking permanently is 15 years.
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