SOLUTION: The SAT Quantitative Test has a population mean of 500 and a population standard deviation of 100. Suppose you randomly select a sample of 25 participants and administer the SAT Q

Question 523804: The SAT Quantitative Test has a population mean of 500 and a population standard deviation of 100. Suppose you randomly select a sample of 25 participants and administer the SAT Quantitative Test to each participant.
a. What would you expect the mean of this sample to be? _________________
b. What is the standard error of the mean for samples of size 25 from this population?
____________________
c. What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score greater than 530?
____________________
d. What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score less than 480?
____________________
e. What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score between 485 and 525?
_____________________
f. Suppose we obtain a mean SAT Quantitative Score of 515. What is the 95% confidence interval for these data?
_____________________

g. Supposed we obtain a mean SAT Quantitative Score of 487. What is the 80% confidence interval for these data?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The SAT Quantitative Test has a population mean of 500 and a population standard deviation of 100.
Suppose you randomly select a sample of 25 participants and administer the SAT Quantitative Test to each participant.
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a. What would you expect the mean of this sample to be?:::500
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b. What is the standard error of the mean for samples of size 25 from this population?:::100/sqrt(25) = 20
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c. What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score greater than 530?
--
t(530) = (530-500)/20 = 3/2
P(x-bar) = P(t > 3/2 when df = 24) = 0.0733
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d. What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score less than 480?
---
t(480) = (480-500)/20 = -1
P(x-bar > 480) = P(t < -1 when df = 24) = 0.1636
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e. What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score between 485 and 525?
Find the t-scores and find that probability between them_____________________
f. Suppose we obtain a mean SAT Quantitative Score of 515. What is the 95% confidence interval for these data?
x-bar = 515
ME = 2.06*20 = 41.28
95% CI: 515-41.28 < u < 515+41.28
_____________________
g. Supposed we obtain a mean SAT Quantitative Score of 487. What is the 80% confidence interval for these data?
487-ME < u < 487+ME
ME = 1.32*20 = 26.36
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Cheers,
Stan H.
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