Question

A manufacturer sells metal bars. Their longest bar is designed to be 10’ long (120 inches). The quality control department randomly collects 41 bars from the production line and measures their length. These 41 bars had an average length of 120.3 inches with a standard deviation of 1.05 in. assume the lengths of the bars are normally distributed.

Conduct the appropriate 95% confidence interval to determine if the standard deviation of the lengths of bars is less than 2.51 inches.

Answer 1

Answer:

Given,

sample n = 41

degree of freedom = n - 1 = 41 - 1 = 40

standard deviation = 1.05

sqrt((n-1)s^2/(alpha/2)) < < sqrt((n-1)s^2/(1 - alpha/2))

substitute values

sqrt((41-1)1.05^2 / 59.342) < < sqrt((41-1)1.05^2 / 24.433)

0.8621 < < 1.3435

0.86 < < 1.34

Here CI doesn't contain 2.51, so we conclude that sd of length < 2.51 inches.