Answer to Question #113206 in Statistics and Probability for Jennie

Question

The breaking strengths of cables produced by a manufacturer have mean 1800 lb and standard deviation 100 lb. By a new technique in the manufacturing process it is claimed that the breaking strength can be increased. To test the claim, a sample of 50 cables is tested, and it is found that the mean breaking strength is 1850 lb. (a) Can you support the claim at 0.01 level of significance? (b) What is the P value of the test?

Answer 1

We need check the hypothesis

H₀:μ=1800 vs. H_a:μ>1800

z-test:

z₀=(μ-μ₀)/(σ/$\sqrt{{n}} ​$)=(1850-1800)/(100*$\sqrt{{50}}$ )=3.54

z_cr=z_0.99=2.33

Since z₀>z_cr  it is concluded that the results are highly significant and the claim is supported;

we are 99% confident that the breaking strength can be increased by the new techniques;

P-value=P(z>3.54)=0.0002