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 6.3 years. At α=0.09​,

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).

16.6	8.1	9.7	16.7	22.3	7.4	16.1	10.8
18.2	12.1	12.6	12.7	9.2	7.6	13.1	12.3
21.7	20.3	15.6	12.3	16.1	17.6	17.8	9.6
17.5	16.1	11.4	19.3	13.6	9.3	17.1	20.5

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

A. H0​: μ=13 (claim)

Ha​: μ≠13

B. H0​: μ≥13 ​(claim)

Ha​: μ<13

C. H0​: μ>13

Ha​: μ≤1313 (claim)

D. H0​:μ≠13 ​(claim)

Ha​: μ=13

E. H0​: μ>13 ​(claim)

Ha​: μ≤13

F. H0​: μ≤13 ​(claim)

Ha​: μ>13

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

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

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

P=   ​(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 99​% level of significance.

A. Reject H0. There is sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.

B. Fail to reject H0. There is sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.

C. Fail to reject H0. There is not sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.

D. Reject H0. There is not sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.

Answer 1

a)

A. H0​: μ=13 (claim)

Ha​: μ≠13

b)

population std dev ,    σ =    6.3
Sample Size ,   n =    32
Sample Mean,    x̅ =   14.4156
      
'   '   '
      
Standard Error , SE =   σ/√n =   1.1137
      
Z-test statistic=   (x̅ - µ )/SE =    1.27

c)

p-Value   =   0.204 [excel formula =2*NORMSDIST(z)]

d)

Conclusion:     p-value>α, fail to reject null hypothesis   

e)

confidenc level = 0.99

Level of Significance ,    α =    0.01

z value=   z α/2=   2.5758   [Excel formula =NORMSINV(α/2) ]  
              
Standard Error , SE =   σ/√n =   1.1137      
margin of error ,   E=Z*SE =   2.869     

confidence interval is               
Interval Lower Limit=   x̅ - E =    11.5469      
Interval Upper Limit=   x̅ + E =    17.2843      
confidence interval is (   11.5469   < µ <   17.2843   )

since, µ=13 lies in the confidence interval, so fail to reject Ho

answer : option c)

Fail to reject H0. There is not sufficient evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years