A simple random sample of 200 third-graders in a large school district was chosen to participate in an after-school program to improve reading skills. After completing the program, the children were tested, and 142 of them showed improvement in their reading skills.
a. Find a point estimate for the proportion of third-graders in the school district whose reading scores would improve after completing the program.
b. Construct a 95% confidence interval for the proportion of third-graders in the school district whose reading scores would improve after completing the program.
c. Is it reasonable to conclude that more than 60% of the students would improve their reading scores after completing the program? Explain.
d. The district superintendent wants to construct a confidence interval for the proportion of all elementary schoolchildren in the district whose scores would improve. Should the sample of 200 third-graders be used for this purpose? Explain.
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