In a statistics class, each student surveys a random sample of 20 students to es
ID: 3235629 • Letter: I
Question
In a statistics class, each student surveys a random sample of 20 students to estimate the number of units the students at their college are enrolled in. The college population is 10,000 students. Using their data, each student constructs a 95% confidence interval for , the average number of units the 10,000 students at their college are enrolled in. There are 40 students in the statistics class, so there are 40 different 95% confidence intervals that estimate . Which conclusion is correct? A. About 95% of the 40 confidence intervals will contain , the average number of units the 10,000 students at their college are enrolled in. B. About 5% of the sample means will not be included in the confidence intervals. C. Each student’s 95% confidence interval will contain about 95% of the population. D. About 5% of the raw data in the samples will not be found in these confidence intervals.
Explanation / Answer
If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean. A 95%confidence interval has a 0.95 probability of containing the population mean. 95% of the population distribution is contained in the confidence interval.
Hence answer is A. About 95% of the 40 confidence intervals will contain , the average number of units the 10,000 students at their college are enrolled in.