Question

The owner of Torpid Oaks B&B wanted to know the average distance its guests had traveled. A random sample of 16 guests showed a mean distance of 85 miles with a standard deviation of 32 miles. The 90 percent confidence interval (in miles) for the mean is approximately:

The answer is 71 and 99

My question is: Why do you have to round down to 71 and round up to 99? It is because of the word approximately? Do I do the same with T score?

Answer 1

T critical value at 0.10 significance level with 15 df = 1.753

90% confidence interval is

- t * S / sqrt(n) < < + t * S / sqrt(n)

85 - 1.753 * 32 / sqrt(16) < < 85 + 1.753 * 32 / sqrt(16)

71 < < 99

99% CI is ( 71 , 99 )

The values are given in miles, it is bigger quantity.

So limits are rounded to nearest integer.