Question

Question Set 1: Two Independent Proportions

Reminder: The standard error is computed differently for a two-sample proportion confidence interval and a two-sample proportion hypothesis test.

Researchers are comparing the proportion of University Park students who are Pennsylvania residents to the proportion of World Campus students who are Pennsylvania residents. Data from a sample are presented in the contingency table below.

		Primary Campus		Total
		University Park	World Campus
Pennsylvania Resident	Yes	115	70	185
	No	86	104	190
Total		201	174	375

1. Construct a 95% confidence interval to estimate the difference between the proportion of all University Park students who are Pennsylvania residents and the proportion of all World Campus students who are Pennsylvania residents. If assumptions are met, use the normal approximation method. Show how you checked assumptions. You should not need to do any hand calculations. Use Minitab Express to construct the confidence interval. Remember to copy+paste all relevant Minitab Express output and always clearly identify your final answer. [15 points]

B. Interpret the confidence interval that you computed in part A by completing the following sentence. [5 points]

I am 95% confident that…

C. Use the five-step hypothesis testing procedure given below to determine if there is evidence of a difference between the proportion of University Park students who are Pennsylvania residents and the proportion of World Campus students who are Pennsylvania residents. If assumptions are met, use the normal approximation method. Use Minitab Express. You should not need to do any hand calculations. Remember to copy+paste all relevant Minitab Express output. [30 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p-value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a real-world conclusion

Answer 1

The Minitab output is:

(a) The 95% confidence interval to estimate the difference between the proportion of all University Park students who are Pennsylvania residents and the proportion of all World Campus students who are Pennsylvania residents is between 0.307 and 0.464.

(b) I am 95% confident that the true difference between the proportion of all University Park students who are Pennsylvania residents and the proportion of all World Campus students who are Pennsylvania residents is between 0.307 and 0.464.

(c) n1*p1 = 0.57*201 = 115 10

n1*(1 - p1) = (1 - 0.57)*201 10

n2*p2 = 174*0.40 = 70 10

n2*(1 - p2) = (1 - 0.40)*174 10

All the assumptions are met.

The test statistic is 3.33.

The p-value is 0.001.

Since the p-value (0.001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is evidence of a difference between the proportion of University Park students who are Pennsylvania residents and the proportion of World Campus students who are Pennsylvania residents.