A socialologist take a simple random sample of 300 from the 27,000 students enro

Question

A socialologist take a simple random sample of 300 from the 27,000 students enrolled at a large State University. There are 222 undergraduates and 78 graduate students in the sample so the sample percentage of undergraduates is 222/300 x 100=74%. The sociologist calculates the SE for the sample percentage of undergraduates, gets 2.5% as the result, and write down the following 95% confidence interval 69% to 79%. State whether or not the following statements are true or false:
A. The range from 69 to 79% is an appropriate 95% confidence interval for the percentage of undergraduates in the sample.
B. The 95% is approximately right because the probability histogram for the percentage of undergraduates at the University follow the normal curve closely.
C. In the same semester a second sociologist also takes a sample random sample of 300 students from the University and uses the same procedure as the first sociologist to calculate a confidence interval. The second sociologist will arrive at exactly the same interval as the first one.

Explanation / Answer

A) This is true because margin of error = 1.960*0.025= 0.049635

95% Interval

(0.74-0.049635, 0.74+0.049635)

=(69%, 79%)

b) This one is also correct because the data follows the normal curve

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