Question

SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 462. Assume the population standard deviation is $sigma$ = 117. Part 1 of 4 (a) Construct a 99.9% confidence interval for the mean mathematics SAT score for the entering freshman class. Round the answer to the nearest whole number. A 99.9% confidence interval for the mean mathematics SAT score is 424 < $mu$ < 500 Part 2 of 4 (b) If the sample size were 110 rather than 100, would the margin of error be larger or smaller than the result in part (a)? Explain. The margin of error would be smaller , since an increase in the sample size will decrease the standard error. Part: 2/4 Part 3 of 4 (c) If the confidence levels were 99.5% rather than 99.9%, would the margin of error be larger or smaller than the result in part (a)? Explain. The margin of error would be (Choose one) , since (Choose one) in the confidence level will (Choose one) the critical value $z_{a/2}$.

          SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean
mathematics SAT score to be 462. Assume the population standard deviation is $sigma$ = 117.
Part 1 of 4
(a) Construct a 99.9% confidence interval for the mean mathematics SAT score for the entering freshman class. Round the
answer to the nearest whole number.
A 99.9% confidence interval for the mean mathematics SAT score is 424 < $mu$ < 500
Part 2 of 4
(b) If the sample size were 110 rather than 100, would the margin of error be larger or smaller than the result in part (a)?
Explain.
The margin of error would be smaller , since an increase in the sample size will decrease the
standard error.
Part: 2/4
Part 3 of 4
(c) If the confidence levels were 99.5% rather than 99.9%, would the margin of error be larger or smaller than the result in
part (a)? Explain.
The margin of error would be (Choose one) , since (Choose one) in the confidence
level will (Choose one) the critical value $z_{a/2}$.

SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean
mathematics SAT score to be 462. Assume the population standard deviation is sigma = 117.
Part 1 of 4
(a) Construct a 99.9% confidence interval for the mean mathematics SAT score for the entering freshman class. Round the
answer to the nearest whole number.
A 99.9% confidence interval for the mean mathematics SAT score is 424 < $mu$ < 500
Part 2 of 4
(b) If the sample size were 110 rather than 100, would the margin of error be larger or smaller than the result in part (a)?
Explain.
The margin of error would be smaller , since an increase in the sample size will decrease the
standard error.
Part: 2/4
Part 3 of 4
(c) If the confidence levels were 99.5% rather than 99.9%, would the margin of error be larger or smaller than the result in
part (a)? Explain.
The margin of error would be (Choose one) , since (Choose one) in the confidence
level will (Choose one) the critical value za/2.

Added by Matthew S.

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