Question

You are curious about the average number of yards Matthew Stafford throws for each game for the Detroit Lions. You randomly select 20 games and see that the average yards per game is 273.7 with a standard deviation of 31.64 yards. You want to create a 95% confidence interval for the true average number of yards per game he throws. What is the margin of error for this estimate

Answer 1

The margin of error for this estimate is of 14.79 yards per game.

Explanation:

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

T interval

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

95% 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 - 0.95)/(2) = 0.975`. So we have T = 2.093

The margin of error is:

`M = T(s)/(√(n))`

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

You randomly select 20 games and see that the average yards per game is 273.7 with a standard deviation of 31.64 yards.

This means that
`n = 20, s = 31.61`

What is the margin of error for this estimate?

`M = T(s)/(√(n))`

`M = 2.093(31.61)/(√(20))`

`M = 14.79`

The margin of error for this estimate is of 14.79 yards per game.