Question

A sample of 44 drivers were asked how many miles they drove in a month; the sample mean number of miles was 554.6, and the sample standard deviation was 160. Calculate and interpret a 95% (two-sided) confidence interval for true average number of miles driven in a month for the population of drivers from which the sample was selected?

Answer 1

To calculate a 95% confidence interval for the true average number of miles driven in a month, use the formula CI = sample mean ± (critical value) × (sample standard deviation / √sample size). Plugging in the given values, the 95% confidence interval is (510.44, 598.76).

Step-by-step explanation:

To calculate a 95% confidence interval for the true average number of miles driven in a month for the population of drivers, we can use the formula:

CI = sample mean ± (critical value) × (sample standard deviation / √sample size)

In this case, the sample mean is 554.6, the sample standard deviation is 160, and the sample size is 44. The critical value for a 95% confidence level and a two-sided interval is 1.96.

Plugging in the values, we get:

CI = 554.6 ± (1.96) × (160 / √44) = 554.6 ± 44.16

So the 95% confidence interval for the true average number of miles driven in a month is (510.44, 598.76). This means we are 95% confident that the true average number of miles falls within this range.