Question

The breaking strengths of cables produced by a certain manufacturer have a mean, u, of 1750 pounds, and a standard deviation of 65 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 100 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1754 pounds. Can we support, at the 0.1 level of significance, the claim that the mean breaking strength has increased

Answer 1

We accept the null hypothesis that the breaking strength mean is less and equal to 1750 pounds and has not increased.

Explanation:

The null and alternative hypotheses are stated as

H0: u ≥ 1750 i.e the mean is less and equal to 1750

against the claim

Ha: u > 1750 ( one tailed test) the mean is greater than 1750

Sample mean = x`= 1754

Population mean = u = 1750

Population deviation= σ = 65 pounds

Sample size= n = 100

Applying the Z test

z= x`- u / σ/ √n

z= 1754- 1750 / 65/ √100

z= 4/6.5

z= 0.6154

The significance level alpha = 0.1

The z - value at 0.1 for one tailed test is ± 1.28

The critical value is z > z∝.

so

0.6154 is < 1.28

We accept the null hypothesis that the breaking strength mean is less and equal to 1750 pounds and has not increased.