Question

An SRS of 20 third grade children is selected in Chicago and each is given a test to measure their reading ability. We are interested in a 90% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points. The margin of error associated with the confidence interval is
O 4.64 points.
O 5.62 points.
O 2.68 points.

Answer 1

The margin or error associated with the confidence interval is 5.62 points

The sample size of the third grade children = 20

The confidence interval for the population mean score  = 90%

The mean score = 64 points

The standard deviation = 12 points

The degree of freedom = The sample size - 1

= 20 - 1

= 19

The critical value of t at degree of freedom 19 = ±2.093

The margin error = Critical value of t × $\frac{s}{\sqrt{n} }$

Substitute the values in the equations

The margin error = 2.093 × $\frac{12}{\sqrt{20} }$

= 2.093 × 2.68

= 5.62 points

Therefore, the margin error is 5.62 points

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