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? Pvalue. 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.
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*(1NORMSDIST(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.
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