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.