Question

According to a recent survey by the National Health and Nutrition Examination Survey, the mean height of adult men in the United States is 69.7 inches with a standard deviation of 3 inches. A sociologist believes that taller men may be more likely to be promoted to positions of leadership, so the mean height of male business executives would be greater than the mean heigth of of the entire male population. A SRS of of 100 male business executives has a mean height of 69.9 inches. We assume that the standard deviation of male executive heights is 3 inches.

(a) Find a 95% confidence interval for the mean height of male business executives.
(b) Is the probability that the mean height of male business executives lies in the interval you found in (a) equal to 0.95? Explain your reasoning.
(c) Suppose the sociologist wants a margin of error of 0.25 inches. Determine how large the sample should be in this case.

Answer 1

given data are:-

z critical value for 95% confidence level ,both tailed test be:-

a). a 95% confidence interval for the mean height of male business executives be:-

(b) yes, the probability that the mean height of male business executives lies in the interval you found in (a) equal to 0.95.

as we are 95% confident that the true population mean height will lie within 69.312 and 70.488.Also, the hypothesized mean , 69.7 inches is included in the 95% confidence interval.

c)margin of error (E) = 0.25

the minimum sample size needed be:-

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