The lengths of time (in years) it took a random sample of 32 former smokers to q

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 4.2 years. At = 0.07 , 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).

13.8      18.4      9.9        14.9      11.8      19.3      16.9      8.2

9.3        8.4        22.2      14.1      8.7        22.2      21.2      10.6

7.7        14.3      7.9        9.6        21.1      14.7      22.3      22.4

18.7      17.7      21.9      8.3        17.6      13.7      22.6      11.2

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

A. H0 : > 13 (claim)

Ha : 13

B. H0 : 13 (claim)

Ha : < 13

C. H0 : 13 (claim)

Ha : = 13

D. H0 : = 13 (claim)

Ha : 13

E. H0 : 13 (claim)

Ha : > 13

F. H0 : > 13

Ha : 13 (claim)

(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.)

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 7 % level of significance.

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

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.

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.

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.

Explanation / Answer

a) Our claim is

D. H0 : = 13 (claim)

Ha : 13

b) Using R calculate Z test statistics .

x=c(13.8,18.4,9.9,14.9,11.8,19.3,16.9,8.2,9.3,8.4,22.2,14.1,8.7,22.2,21.2,10.6,7.7,14.3,7.9,9.6,21.1,14.7,22.3,22.4,18.7,17.7,21.9,8.3,17.6,13.7,22.6,11.2)
> Xbar=mean(x)
> mu=13
> SD=4.2
> n=32
> Z=(Xbar-mu)/(SD/sqrt(n))
> Z
[1] 2.761084

P-value -0.005762

Decision : Using p-value we reject the null hypothesis becuse p-values is less than 0.07.

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

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