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 95% level of confidence. For a sample of 695 third graders, the mean words per minute read was 38.3. Assume a population standard deviation of 3.6. 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:

(38.1,88.6)

Step-by-step explanation:

We are given the following in the question:

Sample mean, $\bar{x}$ = 38.3

Sample size, n = 695

Alpha, α = 0.05

Population standard deviation, σ = 3.6

95% Confidence interval:

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

$38.3 \pm 1.96(\frac{3.6}{\sqrt{695}} ) = 38.3 \pm 0.267 = (38.033,38.567) \approx (38.1,88.6)$