The heights of a simple random sample of 400 male high school sophomores in a mi
ID: 3388056 • Letter: T
Question
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.
Explanation / Answer
(a) What is a 95% confidence interval for ? (65.797, 66.603)
(b) The margin of error for the 95% confidence interval would increase.
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