## 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

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 of confidence. For a sample of 1584 third graders, the mean words per minute read was 35.7. Assume a population standard deviation of 3.3. Construct the confidence interval for the mean number of words a third grader can read per minute. Round your answers to one decimal place.

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1 week 2021-11-20T13:12:21+00:00 1 Answer 0 views 0

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

Here for constructing 99% confidence interval we have used One-sample z test statistics as we know about the population standard deviation.

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

99% confidence interval for = [ , ]

= [ , ]

= [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].