The mean SAT score in mathematics is 528. The standard deviation of these scores is 48. A special preparation course claims that the mean SAT score, μ, of its graduates is greater than 528. An independent researcher tests this by taking a random sample of 90 students who completed the course; the mean SAT score in mathematics for the sample was 532. At the 0.01 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 528? Assume that the population standard deviation of the scores of course graduates is also 48. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 528? OYes O No F XI a S P 6 0=0 OSO 020 □□□<>ロ
The mean SAT score in mathematics is 528. The standard deviation of these scores is 48. A special preparation course claims that the mean SAT score, μ, of its graduates is greater than 528. An independent researcher tests this by taking a random sample of 90 students who completed the course; the mean SAT score in mathematics for the sample was 532. At the 0.01 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 528? Assume that the population standard deviation of the scores of course graduates is also 48. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 528? OYes O No F XI a S P 6 0=0 OSO 020 □□□<>ロ
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:The mean SAT score in mathematics is 528. The standard deviation of these scores is 48. A special preparation course claims that the mean SAT score, μ, of its graduates is greater than 528. An independent researcher tests this by taking a random sample of 90 students who completed the course; the mean SAT score in mathematics for the sample was 532. At the 0.01 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 528? Assume that the population standard deviation of the scores of course graduates is also 48.
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.)
- (d) Find the p-value. (Round to three or more decimal places.)
- (e) Can we support the preparation course’s claim that the population mean SAT score of its graduates is greater than 528?
- ○ Yes ○ No
**Diagram:**
There is a diagram at the side displaying various statistical symbols typically used in hypotheses testing:
- μ (mu): Population mean
- σ (sigma): Population standard deviation
- p: p-value
- X̄ (x-bar): Sample mean
- n: Sample size
The test involves calculating the p-value to determine if the difference in mean scores is statistically significant at the 0.01 significance level.
Expert Solution

Step 1
The sample size is 90, sample mean is 532, population mean is 528, and population standard deviation is 48.
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