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: (24.6 , 25.2)

Step-by-step explanation:

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

$\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}.$

, 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 :

$24.9\pm (1.645)\dfrac{5.1}{\sqrt{837}}\\\\ 24.9\pm (1.645)(0.176281788104)\\\\=24.9\pm0.289983541431\\\\\approx24.9\pm0.3\\\\=(24.9-0.3,\ 24.9+0.3)\\\\=(24.6,\ 25.2)$

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

Answer 2

Answer:we are 90% confident that

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

Step-by-step 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.