Question

he college board sat college entrance exam consists of two sections: math and evidence-based reading and writing (ebrw). sample data showing the math and ebrw scores for a sample of students who took the sat follow. click on the datafile logo to reference the data. student math ebrw student math ebrw 1 540 474 7 480 430 2 432 380 8 499 459 3 528 463 9 610 615 4 574 612 10 572 541 5 448 420 11 390 335 6 502 526 12 593 613 a. use a level of significance and test for a difference between the population mean for the math scores and the population mean for the ebrw scores. what is the test statistic? enter negative values as negative numbers. round your answer to two decimal places. what is the -value? round your answer to four decimal places. what is your conclusion? reject . we cannot conclude that there is a significant difference between the population mean scores for the sat math test and the sat writing test. do not reject . we cannot conclude that there is a significant difference between the population mean scores for the sat math test and the sat writing test. reject . we can conclude that there is a significant difference between the population mean scores for the sat math test and the sat writing test. do not reject . we can conclude that there is a significant difference between the population mean scores for the sat math test and the sat writing test. - select your answer - b. what is the point estimate of the difference between the mean scores for the two tests? what are the estimates of the population mean scores for the two tests? math test ebrw test which test reports the higher mean score? - select your answer -

Answer 1

In statistical terms, the z-score for a SAT math score of 720 is approximately 1.74, indicating a performance above the mean. A score of 1.5 standard deviations above the mean SAT score equates to about 692.5. To see who performed better relative to the others in the SAT or ACT, z-scores of both tests are compared, with the higher z-score indicating a relatively better performance.

Step-by-step explanation:

This question requires a statistical analysis to compare mean scores of two related samples and to interpret z-scores and their significance in the context of the SAT math section. We begin by computing a z-score for a given SAT math score, then we find what score corresponds to a certain number of standard deviations above the mean, and finally, we compare scores from two different standardized tests.

To calculate the z-score for an SAT score of 720, use the formula z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. For μ = 520 and σ = 115, we get z ≈ (720 - 520) / 115 ≈ 1.74. The z-score of 1.74 means the score of 720 is 1.74 standard deviations above the mean.

A math SAT score that is 1.5 standard deviations above the mean is computed as 520 + 1.5(115) ≈ 692.5. This score is significantly higher than the average score and indicates a strong performance relative to the typical test-taker.

To determine who did better with respect to the test each person took, convert both SAT and ACT scores to their respective z-scores and compare these. For SAT: zSAT = (700 - 514) / 117 ≈ 1.59. For ACT: zACT = (30 - 21) / 5.3 ≈ 1.70. The person with the higher z-score performed relatively better. In this case, the student taking the ACT outperformed the one taking the SAT.