Question

A researcher is going to estimate the average typing speed of students of a college. He selects a random sample of 20 students and finds the average typing speed of 70 wpm and the standard deviation of 5 wpm. Estimate the lower bound of the 80% confidence interval of the average typing speed of a student of this college. Express your answer using THREE decimal places

Answer 1

The lower bound of the 80% confidence interval of the average typing speed of a student of this college is of 68.516 words per minute.

Explanation:

We have the standard deviation for the sample, which means that the t-interval 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 = 20 - 1 = 19

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.8)/(2) = 0.9`. So we have T = 1.328

The margin of error is:

`M = T(s)/(√(n)) = 1.328(5)/(√(20)) = 1.484`

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 70 - 1.484 = 68.516 wpm.

The lower bound of the 80% confidence interval of the average typing speed of a student of this college is of 68.516 words per minute.