Question

In a destructive test of product quality, a briefcase manufacturer places each of a simple random sample of the day’s production in a viselike device and measures how many pounds it takes to crush the case. From past experience, the standard deviation has been found to be 21.5pounds. For 35 cases randomly selected from today’s production, the average breaking strength was 341.0 pounds. The lower confidence limit of 99% confidence interval for the mean breaking strength of the briefcases produced today would equal to;

Answer 1

The lower confidence limit of 99% confidence interval for the mean breaking strength of the briefcases produced today would be equal to 331.09 pounds.

Explanation:

Lower limit of confidence interval = mean - Error margin (E)

mean = 341.0 pounds

sd = 21.5 pounds

n = 35

degree of freedom = n - 1 = 35 - 1 = 34

confidence level = 99%

t-value corresponding to 34 degrees of freedom and 99% confidence level is 2.728

E = t × sd/√n = 2.728 × 21.5/√35 = 9.91 pounds

Lower limit = 341.0 - 9.91 = 331.09 pounds