Question

A yoga instructor wanted to construct a 95% confidence interval for the average age of students in her yoga class. She randomly selected 9 students. Their average age was 19.1 years with a standard deviation of 1.5 years. What is the 95% confidence interval for the population mean

Answer 1

The 95% confidence interval for the population mean is between 17.9 and 20.3 years.

Explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 9 - 1 = 8

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.95)/(2) = 0.975`. So we have T = 2.306

The margin of error is:

`M = T(s)/(√(n)) = 2.306(1.5)/(√(9)) = 1.2`

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 19.1 - 1.2 = 17.9 years.

The upper end of the interval is the sample mean added to M. So it is 19.1 + 1.2 = 20.3 years.

The 95% confidence interval for the population mean is between 17.9 and 20.3 years.