Chapter 8: Q 70. (page 542)

Reading scores in Atlanta The Trial Urban District Assessment (TUDA) is a
government-sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from $0$ to $500$ . A score of $243$ is a “basic” reading level and a score of $281$ is “proficient.” Scores for a random sample of $1470$ eighth-graders in Atlanta had a mean of $240$ with standard deviation of $42.17 .$
a. Construct and interpret a $99 %$ confidence interval for the mean reading test score of all Atlanta eighth-graders.
b. Based on your interval from part (a), is there convincing evidence that the mean reading test score for all Atlanta eighth-graders is less than the basic level? Explain your answer.

Expert verified

a. Confidence Interval is $(237.163, 242.837)$

b. Yes, there is convincing evidence that the mean reading test score for all Atlanta eighth-graders is less than the basic level

Step by step solution

It is given that $n = 1470$

$(\bar{x}) = 240$

$(s) = 42.17$

It can be calculated as $C I = \bar{x} \pm t_{α / 2, d f} \times \frac{s}{\sqrt{n}}$

As population standard deviation is not known, we use $t$ confidence interval.

Output of Excel is:

Hence, confidence interval is $(237.163, 242.837)$

So, there is $99 %$ confidence that mean reading score is between $237.163 and 242.837 .$

Confidence Interval is $(237.163, 242.837)$ . Mean reading score is $243$ . It lie between the interval $237.163 and 242.837$ .

Hence, we can say that mean reading score is less than basic level score.

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