Question

7)

A researcher is studying the heights of men with a certain medical condition. She collects a sample of 34 such men and finds the mean height of the sample to be x̄ = 67.6 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.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 67.6

Population standard deviation =    = 2.8

Sample size = n = 34

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_0.005 = 2.576

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

= 2.576 * ( 2.8 /  34 )

= 1.24

At 99% confidence interval estimate of the population mean is,

  ± E

67.6 ± 1.24

( 66.36, 68.84 )  

b) right point = 68.84