Question

You are in charge of reviewing applications for your academic stitution. As a preliminary measure, you want to review only the top 25% of applicants on the basis of standardized test scores. How does calculating the z-score provide additional information regareding how each subject did overall? Provide specific examples of how you would use the information and interpret the scores.

Answer 1

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Explanation:

As the person in charge of reviewing applications for your academic institution, you want to identify the top 25% of applicants based on their standardized test scores. Calculating the z-score can provide additional information regarding how each applicant did overall by comparing their individual scores to the mean and standard deviation of the entire group of test-takers. Here's how you can use the z-score information:

1. Calculate the z-score: To calculate the z-score for each applicant's test score, subtract the mean test score from the individual score and divide the result by the standard deviation of the test scores. The formula is (X - mean) / standard deviation, where X represents the individual score.

2. Interpret the z-score: The z-score represents the number of standard deviations an individual's test score is above or below the mean. A positive z-score indicates a score above the mean, while a negative z-score indicates a score below the mean. The magnitude of the z-score indicates how far an individual's score is from the mean.

3. Use the z-score for ranking: Once you have calculated the z-scores for all applicants, you can rank them based on their z-scores. Applicants with higher z-scores are considered to have performed better compared to the mean, while those with lower z-scores performed below the mean. In this case, you would select the top 25% of applicants with the highest z-scores for further review.

For example, let's say the mean test score is 80 with a standard deviation of 10. If an applicant scored 90 on the test, their z-score would be (90 - 80) / 10 = 1. Similarly, if another applicant scored 70, their z-score would be (70 - 80) / 10 = -1. These z-scores indicate that the first applicant scored 1 standard deviation above the mean, while the second applicant scored 1 standard deviation below the mean.

By using the z-scores, you can compare applicants' performances relative to the overall distribution of scores. This helps you identify the top performers and make informed decisions during the application review process.