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

(38.1,88.6)

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)(\sigma)/(√(n))`

Putting the values, we get,

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

`38.3 \pm 1.96((3.6)/(√(695)) ) = 38.3 \pm 0.267 = (38.033,38.567) \approx (38.1,88.6)`