Question

In: Statistics and Probability

The heights of a simple random sample of 400 male high school sophomores in a Midwestern...

The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured. The sample mean is = 66.2 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of σ = 4.1 inches. What is a 95% confidence interval for µ?

A. (59.46, 72.94)
B. (58.16, 74.24)
C. (65.80, 66.60)
D. (65.86, 66.54)

Expert Solution

= Solution :

Given that,

Point estimate = sample mean = =66.2

Population standard deviation = = 4.1

Sample size n =400

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z/2 * ( / $\sqrt$ n)

= 1.96* ( 4.1/ $\sqrt$ 400 $\sqrt$ )

= 0.40
At 95% confidence interval
is,

- E < < + E

66.2 - 0.40 < < 66.2 + 0.40

(65.80, 66.60)

orchestra answered 2 years ago

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