Question

The lengths of time​ (in years) it took a random sample of

3232

former smokers to quit smoking permanently are listed. Assume the population standard deviation is

6.96.9

years. At

alphaαequals=0.020.02​,

is there enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is

1414

​years? Complete parts​ (a) through​ (e).

10.810.8	19.519.5	8.18.1	17.117.1	20.320.3	13.613.6	8.68.6	16.516.5
20.320.3	7.77.7	20.720.7	13.713.7	16.716.7	21.221.2	15.615.6	8.38.3
16.716.7	21.921.9	22.422.4	12.212.2	18.418.4	17.917.9	7.27.2	20.820.8
16.916.9	13.713.7	10.610.6	11.911.9	22.622.6	12.112.1	22.522.5	14.314.3

​(a) Identify the claim and state the null hypothesis and alternative hypothesis.

A.

Upper H 0H0​:

muμnot equals≠1414

​(claim)

Upper H Subscript aHa​:

muμequals=1414

B.

Upper H 0H0​:

muμequals=1414

​(claim)

Upper H Subscript aHa​:

muμnot equals≠1414

C.

Upper H 0H0​:

muμgreater than>1414

​(claim)

Upper H Subscript aHa​:

muμless than or equals≤1414

D.

Upper H 0H0​:

muμgreater than or equals≥1414

​(claim)

Upper H Subscript aHa​:

muμless than<1414

E.

Upper H 0H0​:

muμgreater than>1414

Upper H Subscript aHa​:

muμless than or equals≤1414

​(claim)

F.

Upper H 0H0​:

muμless than or equals≤1414

​(claim)

Upper H Subscript aHa​:

muμgreater than>1414

​(b) Identify the standardized test statistic. Use technology.

zequals=. 08.08  

​(Round to two decimal places as​ needed.)

​(c) Find the​ P-value. Use technology.

Pequals=. 161.161

​(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

22​%

level of significance.

A.

Fail to rejectFail to reject

Upper H 0H0.

There

is notis not

sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is

1414

years.

B.

RejectReject

Upper H 0H0.

There

isis

sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is

1414

years.

C.

RejectReject

Upper H 0H0.

There

is notis not

sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is

1414

years.

D.

Fail to rejectFail to reject

Upper H 0H0.

There

isis

sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is

1414

years.

        More

Click to select your answer(s).

Answer 1

(A) we want to test whether the mean time it takes smokers to quit smoking permanently is 14 years or not. So, it is a two tailed hypothesis

option B is correct

(B) and (C) are already answered

(D) Fail to reject the null hypothesis because the p value is greater than the significance level 0.02

(E) Since the p value is greater than the significance level of 0.02, we can conclude that there is insufficient evidence to warrant the rejection of the claim

option A is correct