Question

a manufacturer must test that his bolts are 1.00cm long when they come off the assembly line. he must recalibrate his machines if the bolts are too long or too short. after sampling 49 randomly selected bolts off the assembly line, he calculates the sample mean to be 1.08cm . he knows that the population standard deviation is 0.26cm . assuming a level of significance of 0.01 , is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?

Answer 1

Yes, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

The sample mean of 1.08cm is significantly different from the target value of 1.00cm at a level of significance of 0.01.

This means that there is less than a 1% chance that the observed sample mean of 1.08cm could have occurred by chance if the true population mean were actually 1.00cm.

In addition, the p-value for this test is less than 0.01.

This means that we reject the null hypothesis that the true population mean is 1.00cm and conclude that the true population mean is different from 1.00cm.

Therefore, we can be confident that the manufacturer's machines are not producing bolts that are the correct length.

The machines need to be recalibrated to ensure that the bolts are produced at the target length of 1.00cm.