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A sociologist takes 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 writes down the following 95%-confidence interval: 69% to 79%.
Say whether the following statements are true or false.
The range from 69% to 79% is an approximate 95% confidence interval for the percentage of undergraduates in the sample.
The 95% confidence interval is (approximately) right because the probability histogram for the percentage of undergraduates at the university follows the normal curve closely.
In the same semester, a second sociologist also takes a simple 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 confidence interval as the first one.
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