The heights of a simple randomsample of 400male high school sophomores in amidwesternstate are measured. The sample mean is ¯ x = 66.2 inches. Suppose that the heights of malehigh school sophomores follow a Normal distribution with a standard deviation of = 4.1inches.(a) What is a 95% confidence interval for μ?(b) Suppose the heights of a simple random sample of 100 male sophomores were measuredrather 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 becausethe level of confidence has not changed.• The standard deviation would decrease.
The heights of a simple randomsample of 400male high school sophomores in amidwestern
state are measured. The sample mean is ¯ x = 66.2 inches. Suppose that the heights of male
high school sophomores follow a
inches.
(a) What is a 95% confidence interval for μ?
(b) Suppose the heights of a simple random sample of 100 male sophomores were measured
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.
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