Place bounds on the p-value of the test. Engin.

Edu. 7.7 A large public school system was evaluating its elementary school reading program. In particular, educators were interested in the performance of students on a standardized reading test given to all third graders in the state. The mean score on the test was compared to the state average to determine the school system’s rating. Also, the educators were concerned with the variation in scores. If the mean scores were at an acceptable level but the variation was high, this would indicate that a large proportion of the students still needed remedial reading programs. Also, a large variation in scores might indicate a need for programs for those students at the gifted level. Without accelerated reading programs, these students lose interest during reading classes. To obtain information about students early in the school year the statewide test is given during the last month of the school year, a random sample of 150 third-grade students was given the exam used in the previous year. The possible scores on the reading test range from 0 to 100. The data are summarized here. Descriptive Statistics for Reading Scores Variable N Mean Median TrMean StDev SE Mean Reading 150 70.571 71.226 70.514 9.537 0.779 Variable Minimum Maximum Q1 Q3 Reading 44.509 94.570 65.085 76.144

a. Does the plot of the data suggest any violation of the conditions necessary to use the chi-

square procedures for generating a confidence interval and a test of hypotheses about ? b. Estimate the variation in reading scores using a 99 confidence interval. c. Do the data indicate that the variation in reading scores is greater than 90, the variation for all students taking the exam the previous year? s 95 85 75 65 55 45 Reading scores

7.8 Place bounds on the p-value of the test in Exercise 7.7. Engin.

7.9 Baseballs vary somewhat in their rebounding coefficient. A baseball that has a large rebound coefficient will travel further when the same force is applied to it than a ball with a smaller coeffi- cient. To achieve a game in which each batter has an equal opportunity to hit a home run, the balls should have nearly the same rebound coefficient. A standard test has been developed to measure the rebound coefficient of baseballs. A purchaser of large quantities of baseballs requires that the mean coefficient value be 85 units and the standard deviation be less than 2 units. A random sample of 81 baseballs is selected from a large batch of balls and tested. The data are summarized here. Descriptive Statistics for Rebound Coefficient Data Variable N Mean Median TrMean StDev SE Mean Rebound 81 85.296 85.387 85.285 1.771 0.197 Variable Minimum Maximum Q1 Q3 Rebound 80.934 89.687 84.174 86.352