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 90% level of confidence. For a sample of 837 third graders, the mean words per minute read was 24.9. Assume a population standard deviation of 5.1. 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

Answer:we are 90% confident that

the mean number of words a third grader can read per minute is between 24 and 25

Explanation:

Sample size n=837

Sample mean x bar= 24.9

Standard deviation , sigma= 5.1

And the formulae;

See attached picture for the solution.

Answer 2

Answer: (24.6 , 25.2)

Explanation:

Formula to find the confidence interval for population mean (
`\mu`) is given by :-

`\overline{x}\pm z^*(\sigma)/(√(n)).`

, where
`\overline{x}` = Sample mean

z* = Critical z-value. (By z-table)

`\sigma` = Population standard deviation.

n= Sample size.

As per given , we have

`\overline{x}=24.9`

`\sigma=5.1`

n= 837

The critical value for 90% confidence interval : z* = 1.645 (By z-table)

The confidence interval for the mean number of words a third grader can read per minute will be :

`24.9\pm (1.645)(5.1)/(√(837))\\\\ 24.9\pm (1.645)(0.176281788104)\\\\=24.9\pm0.289983541431\\\\\approx24.9\pm0.3\\\\=(24.9-0.3,\ 24.9+0.3)\\\\=(24.6,\ 25.2)`

∴ The confidence interval for the mean number of words a third grader can read per minute= (24.6 , 25.2)