Question

1. 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 21.5 pounds. 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

Solution :

Given that,

= 341

= 21.5

n = 35

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( /n)

=2.576 * (21.5 / 35)

= 9.36

At 99% lower bound  confidence interval n is,

- E

341-9.36

331.6

The lower confidence limit of 99% confidence interval for the mean breaking strength of the briefcases produced today would equal to 331.6