Question

the mean age when smokers first start is 13 years old with a population standard deviation of 1.8 years. a researcher thinks that 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 33 smokers found that their mean starting age was 12.3 years old. do the data support the claim at the 5% significance level? what are the correct hypotheses? ( h_0: mu=13 ) years ( h_1: mu
eq13 ) years based on the hypotheses, find the following: test statistic = (give answer to at least 4 decimal places) critical values ( =pm ) (give answer to at least 4 decimal places) based on the above we choose to select an answer the correct summary would be: select an answer that the claim that the mean age smokers first start is different than 13.

Explanation:

Step1: Calculate the test statistic

The formula for the z - test statistic in a one - sample z - test is \(z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).
Here, \(\bar{x} = 12.3\), \(\mu=13\), \(\sigma = 1.8\), and \(n = 33\).

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Step2: Find the critical values

For a two - tailed test with a significance level of \(\alpha=0.05\), the critical values are \(z_{\alpha/2}\) and \(-z_{\alpha/2}\).
Using the standard normal distribution table or a calculator, \(z_{0.025}=1.9600\) and \(-z_{0.025}=- 1.9600\)

Answer:

• Test Statistic: \(-2.2342\)
• Critical Values: \(\pm1.9600\)
• Since \(|z|=2.2342>1.9600\), we reject the null hypothesis.
• The correct summary is that there is sufficient evidence to support the claim that the mean age smokers first start is different than 13.