SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 438. Assume the population standard deviation is o = 114. Part: 0 / 4 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 Part: 1 / 4 Part 2 of 4 The margin of error would be larger size will increase decrease increase (b) If the sample size were 75 rather than 100, would the margin of error be larger or smaller than the result in part (a)? Explain. Part: 2 / 4 Part 3 of 4 ▼ , since an increase the standard error. The margin of error would be smaller confidence level will increase < p < in the sample the critical value Za/2¹ X ▼ since a decrease Y in the (c) If the confidence levels were 90% rather than 99.9%, would the margin of error be larger or smaller than the result in part (a)? Explain. X 3 X E C
SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 438. Assume the population standard deviation is o = 114. Part: 0 / 4 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 Part: 1 / 4 Part 2 of 4 The margin of error would be larger size will increase decrease increase (b) If the sample size were 75 rather than 100, would the margin of error be larger or smaller than the result in part (a)? Explain. Part: 2 / 4 Part 3 of 4 ▼ , since an increase the standard error. The margin of error would be smaller confidence level will increase < p < in the sample the critical value Za/2¹ X ▼ since a decrease Y in the (c) If the confidence levels were 90% rather than 99.9%, would the margin of error be larger or smaller than the result in part (a)? Explain. X 3 X E C
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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![**SAT Scores Analysis**
A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 438. Assume the population standard deviation is σ = 114.
**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.
99.9% confidence interval for the mean mathematics SAT score is:
\[ \, < \mu < \, \]
**Part 2 of 4**
*(b)* If the sample size were 75 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 **larger**, since a **decrease** in the sample size will **increase** the standard error.
**Part 3 of 4**
*(c)* If the confidence levels were 90% 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 **smaller**, since a **decrease** in the confidence level will **decrease** the critical value \( z_{\alpha/2} \).
**Part 4 of 4**
*(d)* Based on the confidence interval constructed in part (a), is it likely that the mean mathematics SAT score for the entering freshman class is less than 396?
It is **not** likely that the mean mathematics SAT score for the entering freshman class is less than 396.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3bd49ae7-8b45-446c-8381-0655d7ffd02d%2Fc5a51875-d3ef-4cec-8184-2d0da3d939ba%2F95xz2s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**SAT Scores Analysis**
A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 438. Assume the population standard deviation is σ = 114.
**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.
99.9% confidence interval for the mean mathematics SAT score is:
\[ \, < \mu < \, \]
**Part 2 of 4**
*(b)* If the sample size were 75 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 **larger**, since a **decrease** in the sample size will **increase** the standard error.
**Part 3 of 4**
*(c)* If the confidence levels were 90% 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 **smaller**, since a **decrease** in the confidence level will **decrease** the critical value \( z_{\alpha/2} \).
**Part 4 of 4**
*(d)* Based on the confidence interval constructed in part (a), is it likely that the mean mathematics SAT score for the entering freshman class is less than 396?
It is **not** likely that the mean mathematics SAT score for the entering freshman class is less than 396.
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