Question

A tire producer wants to test whether the mean diameter of the tires produced on a given day equals 36 inches. The firm chooses a random sample of 48 tires, and finds that the sample mean diameter is 36.4 inches and the sample standard deviation is 0.8 inches. Create a 90% confidence interval.

Answer 1

df = n - 1 = 48 - 1 = 47

t critical value at 0.10 significance level with 47 df = 1.678

90% confidence interval for is

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

36.4 - 1.678 * 0.8 / sqrt(48) < < 36.4 + 1.678 * 0.8 / sqrt(48)

36.2062 < < 36.5938

90% CI is ( 36.2062 , 36.5938 )