Question

The average number of miles that 90 truckers drove in a day was 540 with a standard deviation of 40 miles. What is the99% confidence interval of the true mean number of miles driven by all truckers?

Answer 1

Degrees of freedom = n - 1 = 90 - 1 = 89

For 89 degrees of freedom and 99% confidence interval,

Critical t value = 2.632

Hence,

99% confidence interval will be:

$540 \pm 2.632*40/\sqrt{90}$

$540 \pm 11.10$

(528.90, 551.10)

Hence,

We are 99% confident that the true average number of miles driven by all truckers will lie between 528.90 miles and 551.10 miles.