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 5.3 years. At alphaequals0.08​, 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). 14.6 9.6 22.3 14.8 14.6 11.7 10.9 16.6 21.7 11.7 19.3 18.4 16.2 17.5 20.3 7.6 16.1 13.3 13.3 11.4 12.6 19.3 7.8 11.7 18.5 11.8 8.5 16.5 14.6 8.2 9.7 16.3 ​(a) Identify the claim and state the null hypothesis and alternative hypothesis. A. Upper H 0​: mugreater than13 ​(claim) Upper H Subscript a​: muless than or equals13 B. Upper H 0​: munot equals13 ​(claim) Upper H Subscript a​: muequals13 C. Upper H 0​: muless than or equals13 ​(claim) Upper H Subscript a​: mugreater than13 D. Upper H 0​: muequals13 ​(claim) Upper H Subscript a​: munot equals13 Your answer is correct.E. Upper H 0​: mugreater than13 Upper H Subscript a​: muless than or equals13 ​(claim) F. Upper H 0​: mugreater than or equals13 ​(claim) Upper H Subscript a​: muless than13 ​(b) Identify the standardized test statistic. Use technology. zequals 1.38  ​(Round to two decimal places as​ needed.) ​(c) Find the​ P-value. Use technology. P= ​(Round to three decimal places as​ needed.)

Answer 1

Solution:

Given:

Sample size = n = 32

Population Standard Deviation =

Claim: the mean time it takes smokers to quit smoking permanently is 13 ​years.

Part a) Identify the claim and state the null hypothesis and alternative hypothesis

Since claim is non directional ,this is two tailed test.

Thus correct option is D.

Vs

Part b) Identify the standardized test statistic. Use technology.

Use TI 84 plus calculator.

Step 1) Press STAT and select EDIT

Step 2) Under EDIT select L1 column and delete all old numbers and enter new numbers given in this question.

Step 3) Again press STAT and select TESTS

Step 4) Select Z test and under Z test select DATA

Enter the numbers and for List L1 is there, if not then Press 2ND and 1 to get L1 there.

Click on Calculate and press Enter

Thus we get following output:

z test statistic = 1.38

Part c) P-value

P-value = 0.167

Since P-value = 0.167 > 0.08 significance level , we fail to reject H0.

thus there is not enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 ​years