Question

A manufacturer produces safety jackets for competitive fencers. These jackets are rated by the minimum force, in newtons, that will allow a weapon to pierce the jacket. When the production process is operating correctly, it produces jackets that have ratings with an average of 840 newtons and a standard deviation of 14 newtons.FIE, the international governing body for fencing, requires jackets to be rated at a minimum of 825 newtons.To check if the process is operating correctly, a manager takes a random sample of 49 jackets from the process, rates them, and calculates the mean rating for jackets in the sample, which turns out to be 830 newtons. She is confident that the standard deviation of the process is at the specified value of 14 newtons.What is the p-value of the appropriate test if she wants to check if the production process currently meets the FIE standards

Answer 1

0

Explanation:

H0 : μ = 840

H1 : μ < 840

Sample size, n = 49

Standard deviation, s = 14

Test statistic = (xbar - μ) ÷ (s/√(n))

Test statistic = (830 - 840) ÷ (14/7)

Test statistic = - 10 / 2

Test statistic = - 5

The Pvalue ;

Pvalue = P(Z < - 5) = 0 (Z probability calculator)

The Pvalue = 0