The manager of the machine-made kretek kretek cigarette company RAENAK found that 12% of its production was below production standards (poor). One day, the manager received a report that on that day 17% of substandard cigarette products were obtained from a random sample of 1000 cigarettes. Test whether the manufacturing defects (17%) are random or permanent (machines need to be repaired)! Use a= 0.05!
The following null and alternative hypotheses for the population proportion needs to be tested:
This corresponds to a right-tailed test, for which a z-test for one population proportion will be used.
Based on the information provided, the significance level is and the critical value for a right-tailed test is
The rejection region for this right-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 proportion is greater than 0.12, at the significance level.
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