Question

A study of the ages of motorcyclists killed in crashes involves the random selection of 137 drivers with a mean of 33.99 years. Assuming that sigma equals 10.6 ​years, construct and interpret a 95​% confidence interval estimate of the mean age of all motorcyclists killed in crashes.

What is the 95​% confidence interval for the population mean μ​?

Notice that the confidence interval limits do not include ages below 20 years. What does this​ mean?

A - The mean age of the population will most likely not be less than 20 years old.

B.

Motorcyclists under the age of 20 never die in crashes.

C.

The mean age of the sample will most likely not be less than 20 years old.

D.

The mean age of the population will never be less than 20 years old.

Answer 1

Given that, sample size ( n )= 137

sample mean = 33.99 years

Population standard deviation = 10.6 years

A 95% confidence level has 0.05 significance level and critical value is,

=> 95% confidence interval for population mean is,

Therefore, the 95​% confidence interval for the population mean μ​ is, (32.215, 35.765) years

Notice that the confidence interval limits do not include ages below 20 years. That means, the mean age of the population will most likely not be less than 20 years old.