The heights of a simple random sample of 400 male high schoo

The heights of a simple random sample of 400 male high school sophomores in a midwestern state are measured. The sample mean is x = 66.2 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of = 4.1 inches.

(a) What is a 95% confidence interval for ?

(b) Suppose the heights of a simple random sample of 100 male sophomores were mea-

sured rather than 400. Which of the following statements is true?

The margin of error for the 95% confidence interval would increase.

The margin of error for the 95% confidence interval would decrease.

The margin of error for the 95% confidence interval would stay the same because the level of confidence has not changed

• The standard deviation would decrease.

Solution

(a) What is a 95% confidence interval for ?   (65.797, 66.603)

(b)   The margin of error for the 95% confidence interval would increase.