Discussion:
Q1) The breaking strengths of cables produced by a certain manufacturer have a mean of 1775 pounds, and a standard deviation of 55 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 90 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1783 pounds. Can we support, at the 0.05 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.)
Perform a one-tailed test.
The null hypothesis:
The alternate hypothesis:
The type of test statistic:
The value of test statistic: (round three decimal places)
The critical value at the 0.05 level of significance:
Can we support the claim that the mean breaking strength has increased?
Q2) An automobile assembly line operation has a scheduled mean completion time of 12.1 minutes. The standard deviation of completion times is 1.3 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 150 completion times under new management was taken. The sample had a mean of 11.8 minutes. Can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed.
Perform a one-tailed test.
The null hypothesis:
The alternate hypothesis:
The type of test statistic:
The value of test statistic:
The p-value(round three decimal places)
Can we support the claim that the mean completion time has decreased under new management? (yes or no)