Problem
Cable Co. manufacturers cables for industrial customers. The industrial customers set the minimum requirement for breaking strength of cables as 285kg. The breaking strength of cables produced by them is currently normally distributed with a mean of =298.32 kg and a standard deviation of a = 5.14 kg. Cable Co. recently made an investment in its manufacturing process for improving the breaking strength.
Assuming that the process mean and standard deviation have not changed by the investment, what is the mean of the sampling distribution for the sample mean X of 11= 32 cables? (Round to 2 decimal places)Assuming that the process mean and standard deviation have not changed by the investment, what is the standard deviation of the sampling distribution (ie., standard error) for the sample mean X of n = 32 cables? (Round to 2 decimal places)In order to evaluate whether the investment actually improved the breaking strength, Cable Co. randomly chose n=32 cables to measure the breaking strength and its sample mean was 300.37 kg. Assuming that the process mean and standard deviation have not changed by the investment, what is the likelihood of observing the sample mean of 300.37 kg? Based on the likelihood computed above, the investment indeed made an improvement in cable breaking strength.