Question

From generation to generation, the mean age when smokers first start to smoke was believed to be 17. A survey of 40 smokers of the millennial generation was done to see if the mean starting age is now different. The sample mean is 18.1 with a sample standard deviation of 1.3. Do the data support that the starting age is now different at the 5% level? Construct 95% confidence interval for the true age and interpre it.

Answer 1

(17.6962, 18.5038)

Since 17 does not lie in this interval, we reject the first start was at age 17.

The confidence interval implies we are 95% confident that for large sample sizes, randomly drawn sample mean will fall within this interval.

Explanation:

Given that from generation to generation, the mean age when smokers first start to smoke was believed to be 17.

A survey of 40 smokers of the millennial generation was done to see if the mean starting age is now different.

The sample mean is 18.1 with a sample standard deviation of 1.3.

We get mean difference =1.1

Std error =
`(1.3)/(√(40) ) \\=0.206`

Z critical value for 95% = 1.96

Margin of error =1.96 ( std error) = 0.40376

Confidence interval

=
`(18.1-0.4038, 18.1+0.4038)\\= (17.6962, 18.5038)`

Since 17 does not lie in this interval, we reject the first start was at age 17.

The confidence interval implies we are 95% confident that for large sample sizes, randomly drawn sample mean will fall within this interval.