Given the following situation, how would you use Megastat to test whether the population defective rate is greater than 10%? Please outline the process for the test and, if necessary, including the output from Megastat to explain your approach. What conditions do you need to check to make sure that the analysis is valid.
"A random sample of 200 cell phones was inspected in a cell phone factory. It was found that 12 of the cell phone is defective in some way. Based on this data, the auditor wants to perform a statistical test to see that the defective rate of cell phone produced by the factory is greater than 10%."
To test whether the population defective rate is greater than 10%, we can use the one-sample proportion test in Megastat. Here is the process to perform the test:
1. Open Microsoft Excel and navigate to the Megastat tab.
2. Click on "Descriptive Statistics" and select "Proportions."
3. In the dialog box, enter the sample size (200) in the "Sample Size" field and the number of defectives (12) in the "Number Success" field.
4. Since we want to test whether the defective rate is greater than 10%, set the "Population Proportion" to 0.10.
5. Under "Hypothesis Testing," select the "Test Proportion" option.
6. Choose the desired significance level (e.g., alpha = 0.05) in the "Test Information" section.
7. Click "OK" to generate the analysis.
The output from Megastat will provide the test statistic, p-value, and confidence interval. To determine whether the population defective rate is greater than 10%, we need to check the following conditions for the analysis to be valid:
1. Random sample: The sample of 200 cell phones should be randomly selected from the entire production process.
2. Independence: Each cell phone in the sample should be independent of one another, meaning that one defective cell phone should not affect the defectiveness of another.
3. Sample size: Megastat will automatically check if the conditions for using normal approximation are met. In general, a sample size of at least 10 successes and 10 failures is necessary for the normal approximation to be valid. In this case, 12 defectives and 188 non-defectives satisfy this condition.
4. Large population assumption: The population from which the sample is drawn should be large enough relative to the sample size. If the factory produces cell phones on a large scale, this condition is likely satisfied.
By satisfying these conditions and following the steps outlined above, we can use Megastat to perform a statistical test to determine whether the defective rate of cell phones produced by the factory is greater than 10%.