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 80% level of confidence. For a sample of 861 third graders, the mean words per minute read was 28.2. Assume a population standard deviation of 5.7. 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 =     = 28.2

Population standard deviation =    = 5.7

Sample size n =861

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.10

Z/2 = Z0.10= 1.28 ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.28 * ( 5.7 / 861 )

= 0.25
At 80% confidence interval mean
is,

- E < < + E

28.2 - 0.25 <   < 28.2+ 0.25

27.95 <   < 28.45