4. A university administrative course scheduler is interested in determining the

Question

4. A university administrative course scheduler is interested in determining the percentage of spring semester students who will attend summer school. She takes a pilot sample of 160 spring semester students and discovers that 56 will return to school in the summer Construct a 96% confidence interval estimate for the percentage of spring semester students who will return to summer school. a. b. What if the sample of students studied was increased to 400, what impact would it have on the interval at a 0.95 probability?

Explanation / Answer

A) P = 56/160 = 0.35

At 96% confidence interval the critical value is 2.05

The confidence interval is

P +/- z* * sqrt(P * (1 - P)/n

= 0.35 +/- 2.05 * sqrt(0.35 * 0.65/160)

= 0.35 +/- 0.077

= 0.273, 0.427

B) As the sample size increases the width of the confidence interval decreases.

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