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 6.1 years. At α = 0.02, 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).Data: 20.4, 7.1, 7.9, 18.9, 20.2, 13.3, 8.8, 20.4, 16.6, 19.5, 8.8, 18.4, 17.7, 15.7, 22.4, 17.6, 8.7, 7.6, 20.7, 12.7, 18.5, 18.6, 15.6, 15.5, 21.7, 12.2, 12.5, 10.5, 9.8, 8.1, 15.7, 8.1(a) Hypothesis Statements:- **A.** $H_0: \mu > 13$ (claim) $H_a: \mu \leq 13$- **B.** $H_0: \mu \leq 13$ (claim) $H_a: \mu > 13$- **C.** $H_0: \mu = 13$ (claim) $H_a: \mu \neq 13$ ✔️- **D.** $H_0: \mu \neq 13$ (claim) $H_a: \mu = 13$- **E.** $H_0: \mu \geq 13$ (claim) $H_a: \mu < 13$- **F.** $H_0: \mu < 13$ (claim) $H_a: \mu \geq 13$(b) Identify the standardized test statistic. Use technology.$z =$ [\_\_\_] (Round to two decimal places as needed.)

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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 6.1 years. At α = 0.02, 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).

Data:
20.4, 7.1, 7.9, 18.9, 20.2, 13.3, 8.8, 20.4, 16.6, 19.5, 8.8, 18.4, 17.7, 15.7, 22.4, 17.6, 8.7, 7.6, 20.7, 12.7, 18.5, 18.6, 15.6, 15.5, 21.7, 12.2, 12.5, 10.5, 9.8, 8.1, 15.7, 8.1

(a) Hypothesis Statements:

- **A.** $H_0: \mu > 13$ (claim)
$H_a: \mu \leq 13$

- **B.** $H_0: \mu \leq 13$ (claim)
$H_a: \mu > 13$

- **C.** $H_0: \mu = 13$ (claim)
$H_a: \mu \neq 13$ ✔️

- **D.** $H_0: \mu \neq 13$ (claim)
$H_a: \mu = 13$

- **E.** $H_0: \mu \geq 13$ (claim)
$H_a: \mu < 13$

- **F.** $H_0: \mu < 13$ (claim)
$H_a: \mu \geq 13$

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

$z =$ [\_\_\_] (Round to two decimal places as needed.)

Expert Solution

Step 1

Given

X be the length (in years) of smoking by farmers

=20.4 , 7.1 , 7.9 , 18.9 , 20.2 , 13.3 , 8.8 , 20.4 , 16.6 , 19.5 , 8.8 , 18.4 , 17.4 , 15.7 , 22.4 , 17.6 ,

8.7 , 7.6 , 20.7 , 12.7 , 18.5 , 15.8 , 18.6 , 15.5 , 21.7 , 12.2 , 12.5 , 10.5 , 9.8 , 8.1 , 15.7 , 8.1

n=sample size = 32

$σ$ = Population standard deviation of years of smoking by farmers =6.1

$μ$ = Population mean of years of smoking b farmers

$\bar{X} b e t h e s a m p l e m e a n$

Step 2

We need to test the claim whether the mean length of time (in years) it take farmers to quit smoking is 13 years

Therefore from the given option OPTION C is correct

That is

$H_{0} : μ = 13 H_{1} : μ \neq 13$

Since this hypothesis tests our claim that whether the mean time is equal or not equal to 13 and not whether it is greater or less than 13.

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