Quality Control (QC) and random sampling play important roles in modern manufacturing. The QC specification for manufacturing a particular component part is that no more than 4.5% of randomly sampled parts can be found defective. Over the course of 30 consecutive shifts, 17 of 249 randomly sampled parts were found defective. a. Compute a 90% confidence interval for the true population proportion, ?, of defective parts. b. Set up the appropriate hypothesis test to determine whether the sample provides strong evidence that the proportion of defective parts exceeds the QC specification. Specifically, state the null hypothesis, the alternative hypothesis, and compute the test statistic. Is this a one-tailed test to the left, a one-tailed test to the right, or a two-tailed test? c. What is the p-value for the test statistic computed in (b)? Also, write the Excel function you used to determine this p-value, including the inputs that you entered in the Excel function (do not give cell references; write in the actual numbers and use quotes on your answer tab to show the details). d. Based on the results from (c), what is your conclusion about the true proportion, ?, of defective parts at α = .05.
Quality Control (QC) and random sampling play important roles in
modern manufacturing. The QC specification for manufacturing a particular component part is that no more than 4.5% of randomly sampled parts can be found defective. Over the course of 30 consecutive shifts, 17 of 249 randomly sampled parts were found defective.
a. Compute a 90% confidence interval for the true population proportion, ?, of defective parts.
b. Set up the appropriate hypothesis test to determine whether the sample provides strong evidence that the proportion of defective parts exceeds the QC specification. Specifically, state the null hypothesis, the alternative hypothesis, and compute the
test statistic. Is this a one-tailed test to the left, a one-tailed test to the right, or a two-tailed test?
c. What is the p-value for the test statistic computed in (b)? Also, write the Excel
d. Based on the results from (c), what is your conclusion about the true proportion, ?, of defective parts at α = .05.
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