Question

The mean breaking strength of cables supplied by a manufacturer is 1,800 with a standard deviation of 100. By a new technique in the manufacturing process it is claimed that the breaking strength of the cables has increased. In order to test this claim a sample of 50 cables is tested. It is found that the mean breaking strength is 1,850. Can you support the claim at 0.01 level of significance?

Answer 1

Given Population mean µ = 1800 

Population SD σ = 100 

Sample size n = 50 

Sample mean \(\overline{x}\)= 1850 

Significance level α = 0.01 

Null hypothesis H₀ : µ = 1800 

(i.e) the breaking strength of the cables has not increased, after the new technique in the manufacturing process.

Alternative hypothesis H₁ : µ > 1800 (i.e) the new technique was successful. 

Test statistic

The table value for the one-tailed test is Zα = 2.33. Comparing the calculated value and table value, we find that Z > Zα (i.e.) 3.536 > 2.33.

Inference: Since the calculated value is greater than the table value at a 1 % level of significance, the null hypothesis is rejected and we accept the alternative hypothesis. We conclude that by the new technique in the manufacturing process the breaking strength of the cables is increased. So the claim is supported at 0.01 level of significance.