Question

32)

A researcher is studying the heights of men with a certain medical condition. She collects a sample of 33 such men and finds the mean height of the sample to be x̄ = 65.1 inches. Assume that the standard deviation of heights of men with the condition is the same as that of the general population, σ = 2.8 inches.

a) Find a 99% confidence interval for the true mean height of the population of mean with this condition.

b) Provide the right endpoint of the interval as your answer.

Round your answer to 2 decimal places.

Please explain each step (even if you are using a ti-84 calculator) in detail. Thank you!

Answer 1

a)

significance level = 1 - 0.99 = 0.01

From Z table,

Critical value Z/2 = 2.576

99% confidence interval for is

- Z/2 * / sqrt(n) < < + Z/2 * / sqrt(n)

65.1 - 2.576 * 2.8 / sqrt ( 33) < < 65.1 + 2.576 * 2.8 / sqrt ( 33)

63.84 < < 66.36

99% CI is ( 63.84 , 66.36 )

b)

Right endpoint = 66.36