A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was 460 with a margin of error of 24. Which of the following is a reasonable value for the true mean SAT score of the graduating high school seniors?
Question
A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was 460 with a margin of error of 24. Which of the following is a reasonable value for the true mean SAT score of the graduating high school seniors?
Solution
The study found that the mean SAT score was 460 with a margin of error of 24. This means that the true mean SAT score could be anywhere from 24 points below 460 to 24 points above 460.
To find the range of reasonable values for the true mean SAT score, we subtract and add the margin of error from the mean score:
- Lower limit: 460 - 24 = 436
- Upper limit: 460 + 24 = 484
So, any value between 436 and 484 would be a reasonable value for the true mean SAT score of the graduating high school seniors.
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