The dropdown has the following: 95(400) 400/95 0.95(400) 400/0.95 Suppose that 4

Question

The dropdown has the following:

95(400)

400/95

0.95(400)

400/0.95

Suppose that 400 statistics students each took a random sample (with replacement) of 100 students at their college and recorded the ages of the students in their sample. Then each student used his or her data to calculate a 95% confidence interval for the mean age of all students at the college. How many of the 400 intervals would you expect to capture the true population mean age, and how many would you expect not to capture the true population mean? Explain by showing your calculation The number of intervals expected to capture the true population mean is Type an integer or a decimal.) The number of intervals expected to not capture the true population mean is Type an integer or a decimal) The expression can be used to find the number of intervals expected to capture the true population mean.

Explanation / Answer

Each student is constructing a 95% confidence interval.

By, 95% confidence interval we mean that we are 95%

confident that the interval will contain the true value of the

population parameter.

The number of intervals expected to capture the true

population mean is = 400 * 0.95 = 380. (Ans).

The number of intervals expected to not capture the true

population mean is = 400 * 0.05 = 20. (Ans).

The expression which is used to determine the number of

intervals expected to capture the population mean is

(0.95 * 400). (Ans).

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