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 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.