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 98% level of confidence. For a sample of 1116 third graders, the mean words per minute read was 28.1. Assume a population standard deviation of 4.2. 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

Solution :

Given that,

$\bar x$ = 28.1

$\sigma$ = 4.2

n = 1116

At 98% confidence level the z is ,

$\alpha$ = 1 - 98% = 1 - 0.98 = 0.02

$\alpha$ / 2 = 0.02 / 2 = 0.01

Z_$\alpha$/2 = Z_0.01 = 2.326

Margin of error = E = Z_$\alpha$/2* ($\sigma$ /$\sqrt$n) = 2.326 * (4.2 / $\sqrt$1116) = 0.3

At 98% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

28.1 - 0.3 < $\mu$ < 28.1 + 0.3

27.8 < $\mu$ < 28.4

(27.8 , 28.4)