Question

A manufacturer has developed a new fishing line, which the company claims has a mean breaking strength of 14.5 kilograms with a standard deviation of 0.8 kilograms. Believing the mean breaking strength is less than what company has claimed, a customer protection agency took a random sample of 40 such fishing lines and found that the mean breaking strength for this sample is 13.2 kilograms. Given the breaking strength of all such lines have a normal distribution, test whether the agency’s suspicion is valid or not at 1% significance level.

Please provide correct answer without using excel formulas.

Answer 1

Here in this scenario manufacturer claim is that the mean breaking strength of fishing line is less than 14.5.

To test this claim we have to use one sample z test because here the population standard deviations is known. Using the sample information we can perform the test at 1% level of significance as below,

The z critical value is calculated using Standerd normal z-table.

Conclusion :

Since z cal test Statistic fall in critical region so we concluded that the null hypothesis Ho is rejected.

Therefore, there is enough evidence to claim that the population mean μ strength of fishing line is less than 14.5, at the 0.01 significance level.

Thank you.