Question: A large public school system was evaluating its elementary school

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.
a. Does the following 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 σ?
b. Estimate the variation in reading scores using a 99% confidence interval.
c. Do the data indicate that the standard deviation in reading scores is greater than 9, the standard deviation for all students taking the exam the previous year? Use α = .01 in reaching your conclusion.

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