Answer to Question #325231 in Statistics and Probability for Fatma

Question

4. The mean breaking strength of the cables supplied by a manufacturer is 1850 with a SD of 100. By a new technique in the manufacturing process, it is claimed that the breaking strength of the cable has increased. To test this claim, a sample of 50 cables is tested and it is found that the mean breaking strength is 1875. Can we support the claim at 1% LOS?

Answer 1

$H_0:\mu=1875$

$H_1: \mu <1875$

Test statistic

$Z=\frac{x-\mu}{\sigma/\sqrt{n}}=\frac{1850-1875}{100/\sqrt{50}}=-1.77$

Critical level at 0.01 is

$Z_{\alpha/2}=Z_{0.005}$ (Find in z table value 1-0.005=0.995) Z=2.58

As |-1.77|<2.58 we can support H₀