SOLUTION: Could someone please help with this?: The SAT math scores for all seniors in a high school are normally distributed with population standard deviation of 200. 100 seniors from

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Question 1051026: Could someone please help with this?:
The SAT math scores for all seniors in a high school are normally distributed with population standard deviation of 200. 100 seniors from the school are randomly selected, and their SAT math scores has a sample mean of 650.
(a) What distribution will you use to determine the critical value for a confidence interval estimate of the mean SAT math score for the seniors in the high school? Why?
(b) Construct a 95% confidence interval estimate of the mean SAT math score for the seniors in the high school. (Show work and round the answer to two decimal places)


(c) Is a 90% confidence interval estimate of the mean SAT math score wider than the 95% confidence interval estimate you got from part (b)? Why? [You don’t have to construct the 90% confidence interval]
Thank you for any help!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
The SAT math scores for all seniors in a high school are normally distributed
with population standard deviation of 200.
n = 100, x̄ = 650
(a)
Find a 95% confidence interval estimate of The mean SAT math score for HS seniors
Population SD Known: will use a z score analysis:
z = invNorm((1-.95)/2) = invNorm(.05)
critical value equal to z = 1.96
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(b )
ME =+z%2Asigma%2Fsqrt%28n%29
ME = 1.96(200/10) = 39.2
650 ± 39.2
We are 95% confident that the mean SAT math score for the seniors is:
between 614.8 and 689.2
Check Arithmetic
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(c) Is a 90% confidence interval estimate of the mean SAT math score wider
than the 95% confidence interval estimate you got from part (b)? NO
Why? 90% confidence interval z = 1.645 (which is <1.96 Multiplying by smaller number)
Less accuracy, smaller interval