Question

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

At the beginning of the Summer 2018 semester, students enrolled in World Campus and University Park WEB sections of STAT 200 completed a survey. Data concerning their primary campus and their employment status are presented in the table below.

		Primary Campus		Total
		World Campus	University Park
Employed Full-Time	Yes	185	70	255
	No	81	341	422
Total		266	411	677

A. Construct a 95% confidence interval to estimate the difference between the proportions of all World Campus and University Park online STAT 200 students who are employed full-time. If assumptions are met, use the normal approximation method. 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. [20 points]

B. Use the five-step hypothesis testing procedure given below to determine if there is evidence of a difference between the proportions of World Campus and University Park WEB students who are employed full-time in the populations. If assumptions are met, use the normal approximation method. You should not need to do any hand calculations. Use Minitab Express to obtain the test statistic and p value. 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

Test and CI for Two Proportions

Method

p₁: proportion where Sample 1 = Event

p₂: proportion where Sample 2 = Event

Difference: p₁ - p₂

Descriptive Statistics

Sample	N	Event	Sample p
Sample 1	266	185	0.695489
Sample 2	411	70	0.170316

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1.Estimation for Difference

Difference	95% CI for Difference
0.525172	(0.458996, 0.591348)

CI based on normal approximation

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2. Test

Sample are independent and normally dist

Null hypothesis	H₀: p₁ - p₂ = 0
Alternative hypothesis	H₁: p₁ - p₂ ≠ 0

Method	Z-Value	P-Value
Normal approximation	15.55	0.000

Reject Ho . P-value is less than 0.05