Estimate the variation in reading scores using a 99

Question

Question 1:

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 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 gift 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. Estimate the variation in reading scores using a 99% confidence interval.

b. 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.

Question 2.

Use data below:

	Summary Data for SAT Reasoning Exams
Testing Method	Sample Size	Mean	Standard Deviation
Computer	91	484.45	53.77
Conventional	91	487.38	36.94

a. Construct a 95% confidence interval for σ₁/σ₂

b. Test hypothesis for σ₁ = σ₂, using α = 0.05

c. Construct a 95% confidence interval for μ₁ - μ₂

d. test hypothesis for μ₁ = μ₂ using α = 0.05

Question 3.

Use data

Environment	Weight (in pounds) of Deer
Wild	114.7	128.9	111.5	116.4	134.5	126.7	120.6	129
Ranch	120.4	91	119.6	119.4	150	169.7	100.9	76.1
Zoo	103.1	90.7	129.5	75.8	182.5	76.8	87.3	77.3

Perform a BFL test using SAS. Present the results in the usual hypothesis test format using α = 0.05