Answer:
99% confidence interval for the true mean number of words a third grader can read per minute is [35.5 , 35.9].
Step-by-step explanation:
We are given that a sample of 1584 third graders, the mean words per minute read was 35.7. Assume a population standard deviation of 3.3.
Firstly, the pivotal quantity for 99% confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample mean words per minute read = 35.7
= population standard deviation = 3.3
n = sample of third graders = 1584
= population mean number of words
<em>Here for constructing 99% confidence interval we have used One-sample z test statistics as we know about the population standard deviation.</em>
<em />
So, 99% confidence interval for the population mean, is ;
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.58 & 2.58}
P(-2.58 < < 2.58) = 0.99
P( <
<
) = 0.99
P( <
<
) = 0.99
<u>99% confidence interval for</u> = [
,
]
= [ ,
]
= [35.5 , 35.9]
Therefore, 99% confidence interval for the true mean number of words a third grader can read per minute is [35.5 , 35.9].