Question

Assume that a sample is used to estimate a population mean μ . Find the 99.9% confidence interval for a sample of size 25 with a mean of 16.9 and a standard deviation of 15.7. Enter your answer accurate to one decimal place. I am 99.9% confident that the mean μ is between ____and____

Answer 1

solution

Given that,

mean = = 16.9

standard deviation = = 15.7

n = 25

= 16.9

= / n = 15.7 /25=3.14

middle 99.9% of score is

P(-z < Z < z) = 0.999

P(Z < z) - P(Z < -z) = 0.999

2 P(Z < z) - 1 = 0.999

2 P(Z < z) = 1 + 0.999 = 1.999

P(Z < z) = 1.999 / 2 = 0.9995

P(Z <3.29 ) = 0.9995

z  ± 3.29 using z table

Using z-score formula  

= z * +   

= ± 3.29 *3.14+16.9

= 6.57 and 27.23