Question

The mean age when smokers first start is 13 years old with a population standard deviation of 2 years. A researcher thinks that the smoking age has significantly changed since the invention of ENDS—electronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. The sample of 30 smokers found that their mean starting age was 12.2 years old. Do the data support the claim at the 5% significance level?

What are the correct hypotheses?

H₀:

H₁:

Based on the hypotheses, find the following:

Test Statistic z = (Give answer to at least 4 decimal places)

Critical Values =± (Give answer to at least 4 decimal places)

Based on the above we choose to .....

a. Reject the null hypothesis

b. Accept the null hypothesis

c. Fail to reject the null hypothesis

The correct summary would be:

a. There is enough evidence to reject the claim

b. There is not enough evidence to reject the claim

c. There is enough evidence to support the claim

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis:H0: μ = 13
Alternative Hypothesis: H1: μ ≠ 13

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (12.2 - 13)/(2/sqrt(30))
z = -2.1909

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.9600 and 1.9600.
Hence reject H0 if z < -1.96 or z > 1.96

Reject the null hypothesis

There is enough evidence to support the claim