A student wanted to quickly construct a 95% confidence interval for the average age of students in her statistics class. She randomly selected 9 students. From the sample she learned their average age was 19.1 years with a sample standard deviation of 1.5 years. What is the 95% confidence interval for the population mean

The 95% confidence interval for the population mean is between 15.641 years and 22.559 years.

Step-by-step explanation:

We are in posession of the sample's standard deviation, so we use the Students t-distribution 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 ). So we have T = 2.3060

The margin of error is:

M = T*s = 2.3060*1.5 = 3.459

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 19.1 - 3.459 = 15.641 years

The upper end of the interval is the sample mean added to M. So it is 19.1 + 3.459 = 22.559 years

The 95% confidence interval for the population mean is between 15.641 years and 22.559 years.

step-by-step explanation: