The purchasing director of an industrial part factory is investigating the possibility of purchasing a new type of milling machine. He determines that the new machine will be bought if there is evidence that the parts produced have a higher mean breaking strength than those from the old machine. The population standard deviation of the breaking strength for the old machine is 10kg and for the new machine is 9 kg. A sample of 100 parts was taken from each machine. Old machine indicates a sample mean of 65kg while new machine indicates a sample mean of 72 kg. Using the 0.01 level of significance, is there evidence that the purchasing director should buy the new machine? (critical value = + 2.575 )
The following null and alternative hypotheses need to be tested:
This corresponds to a left-tailed test, and a z-test for two means, with known population standard deviations will be used.
Based on the information provided, the significance level is and the critical value for a left-tailed test is
The rejection region for this left-tailed test is
The z-statistic is computed as follows:
Since it is observed that
it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value is and since it is concluded that the null hypothesis is rejected.
Therefore, there is enough evidence to claim that the population mean
is less than at the significance level.
Therefore, there is enough evidence to claim that the purchasing director should buy the new machine at the significance level.
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