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

4.24.2

years. At

alpha?equals=0.060.06?,

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).

21.621.6	21.721.7	20.720.7	7.47.4	21.121.1	14.214.2	12.812.8	15.215.2
10.410.4	16.216.2	15.515.5	20.320.3	16.216.2	17.517.5	19.419.4	13.513.5
20.320.3	20.820.8	10.110.1	15.215.2	10.310.3	22.222.2	19.719.7	17.617.6
14.814.8	15.715.7	8.58.5	22.922.9	9.19.1	15.715.7	13.113.1	19.519.5

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

A.

Upper H 0H0?:

mu?less than or equals?1414

?(claim)

Upper H Subscript aHa?:

mu?greater than>1414

B.

Upper H 0H0?:

mu?not equals?1414

?(claim)

Upper H Subscript aHa?:

mu?equals=1414

C.

Upper H 0H0?:

mu?equals=1414

?(claim)

Upper H Subscript aHa?:

mu?not equals?1414

D.

Upper H 0H0?:

mu?greater than>1414

Upper H Subscript aHa?:

mu?less than or equals?1414

?(claim)

E.

Upper H 0H0?:

mu?greater than>1414

?(claim)

Upper H Subscript aHa?:

mu?less than or equals?1414

F.

Upper H 0H0?:

mu?greater than or equals?1414

?(claim)

Upper H Subscript aHa?:

mu?less than<1414

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

zequals=nothing??

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

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

Pequals=nothing

?(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

66?%

level of significance.

A.

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.

B.

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.

C.

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.

D.

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.

Answer 1

We have given data in increasing order will be,
7.4,8.5,9.1,10.1,10.3,10.4,12.8,13.1,13.5,14.2,14.8,15.2,15.2,15.5,15.7,15.7,
16.2,16.2,17.5,17.6,19.4,19.5,19.7,20.3,20.3,20.7,20.8,21.1,21.6,21.7,22.2,22.9
Sample size:32

Mean (x?): 16.225

(a) the null hypothesis and alternative hypothesis.

Option C) is correct.

vs

?(b) the standardized test statistic.

  

=2.99679

  

(c) P value =0.0027..................by using =2*(1-NORMSDIST(3))

(d) Option D) is correct.

D.

Reject H0. There is sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 14 years.