Answer:
99% confidence interval for the mean number of words a third grader can read per minute is [24.7 , 25.1].
Explanation:
We are given that 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 of confidence. For a sample of 4657 third graders, the mean words per minute read was 24.9. Assume a population standard deviation of 5.7.
So, the pivotal quantity for 99% confidence interval for the mean number of words a third grader can read per minute is given by;
P.Q. =
~ N(0,1)
where,
= sample mean words per minute read = 24.9
= population standard deviation = 5.7
n = sample of third graders = 4657
= population mean
So, 99% confidence interval for the population mean,
is ;
P(-2.5758 < N(0,1) < 2.5758) = 0.99
P(-2.5758 <
< 2.5758) = 0.99
P(
<
<
) = 0.99
P(
<
<
) = 0.99
99% confidence interval for
= [
,
]
= [
,
]
= [24.7 , 25.1]
Therefore, 99% confidence interval for the mean number of words a third grader can read per minute is [24.7 , 25.1].