We appreciate your visit to SAT Scores A college admissions officer sampled 124 entering freshmen and found that 35 of them scored less than 530 on the math SAT Tasks. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The SAT score problem involves calculating z-scores, identifying scores at certain standard deviations above the mean, and comparing results across different standardized tests by converting scores to a common scale.
Explanation:
The SAT scores and related statistics problems can be solved using concepts of normal distribution and statistical testing. A point estimate is a single value estimate of a population parameter. In part A, for example, with 35 out of 124 students scoring less than 530, the point estimate would be the proportion, which is 35/124. A confidence interval gives a range of values for our parameter based on the sample statistic and is useful for making inferences about the population parameter. The standard deviation is a measure of the amount of variation or dispersion of a set of values, and the hypothesis test is a method of making decisions or inferences about population parameters.
To calculate the z-score for an SAT score of 720, you would use the formula z = (X - µ) / σ, where X is the score, µ is the mean, and σ is the standard deviation. Using the 2005 data where µ = 520 and σ = 115, the z-score for an SAT score of 720 is z = (720 - 520) / 115 ≈ 1.74. This z-score tells us that 720 is 1.74 standard deviations above the mean.
To find a score that is 1.5 standard deviations above the mean of 520, you multiply 1.5 by the standard deviation of 115 and add it to the mean: 520 + 1.5(115) ≈ 692.5. This score is higher than the average SAT math score.
Comparing scores across different tests such as the SAT and ACT would involve converting scores to a common scale like z-scores or percentiles to determine who performed better relative to others taking the same test.
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