An industrial supplier has shipped a truckload of Teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 10 ounces printed on each cartridge. To check this claim, a sample of n = 10 cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: X = 10.11 ozs., s = .30 ounce.
To determine where the supplier’s claim is true, consider the test, Ho: µ = 10 vs. Ha: µ > 10, where µ is the true mean weight of the cartridges. Find the rejection region for the test using α = .01.
Solution: We need to test
In order to find the rejection region, we need the critical t-value forand 9 degrees of freedom, which is
2.821. Since this is a right-tailed test, the rejection region is
We use Statdisk to apply the test. The results are shown below
Since the t-statistics (1.0541) is less than the critical value, we fail to reject the null hypothesis.