Question

an educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an estimate at the 99% level confidence. For a sample of 2006 third graders, the mean words per minute read was 27.2. assume a population standard deviation of 4.1. construct the confidence interval for the mean number of words a third grader can read per minute. Round your answer to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 27.2

Population standard deviation = = 4.1

Sample size = n = 2006

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (4.1 / 2006 )

= 0.2

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

- E < < + E

27.2 - 0.2 < < 27.2 + 0.2

27.0 < < 27.4

(27.0 , 27.4)