Question

A simple random sample of 20 third-grade children from a certain school district is selected, and each is given a test to measure his/her reading ability. You are interested in calculating a 95% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points.

What is the margin of error associated with the confidence interval?

A. 2.68 points

B. 4.64 points

C. 5.62 points

D. 6.84 point

Answer 1

Option C) 5.62 points

Explanation:

We are given the following in the question:

Sample size, n = 20

Sample mean score = 64

Sample standard deviation, s = 12

Degree of freedom =

`=n-1\\=20-1\\=19`

We have to calculate margin of error for a 95% confidence interval.

Formula for margin of error:

`t_(critical)* \displaystyle(s)/(√(n))`

Putting the values, we get,

`t_(critical)\text{ at degree of freedom 19 and}~\alpha_(0.05) = \pm 2.093`

`2.093* (\displaystyle(12)/(√(20)) )\\\\ =5.6161\approx 5.62`

Thus, the correct answer is

Option C) 5.62 points