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 98% level of confidence. For a sample of 4725 third graders, the mean words per minute read was 27.3. Assume a population standard deviation of 6.3. Construct the confidence interval for the mean number of words a third grader can read per minute. Round your answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean =   = 27.3

Population standard deviation =    = 6.3

Sample size = n = 4725

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

Margin of error = E = Z/2    * ( /n)

= 2.326 * ( 6.3 /   4725 )

= 0.2132
At 98% confidence interval estimate of the population mean
is,

- E < < + E

27.3 - 0.2132 <   < 27.3 + 0.2132

27.0868 <   < 27.5132

( 27.1 , 27.5)