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An IQ test is designed so that the mean is 100 and the standard deviation is 12 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 7 IQ points of the true mean. Assume that o = 12 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. The required sample size is (Round up to the nearest integer.) Would it be reasonable to sample this number of students? Yes. This number of IQ test scores is a fairly large number. No. This number of IQ test scores is a fairly large number. Yes. This number of IQ test scores is a fairly small number. No. This number of IQ test scores is a fairly small number. O 0 0 0

An IQ test is designed so that the mean is 100 and the standard deviation is 12 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 7 IQ points of the true mean. Assume that o = 12 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. The required sample size is (Round up to the nearest integer.) Would it be reasonable to sample this number of students? Yes. This number of IQ test scores is a fairly large number. No. This number of IQ test scores is a fairly large number. Yes. This number of IQ test scores is a fairly small number. No. This number of IQ test scores is a fairly small number. O 0 0 0

MATLAB: An Introduction with Applications
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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**Title: Determining Sample Size for Estimating Mean IQ Scores** **Introduction:** An IQ test is designed such that the mean is 100 and the standard deviation is 12 for the population of normal adults. This task involves finding the sample size necessary to estimate the mean IQ score of statistics students with 99% confidence that the sample mean is within 7 IQ points of the true mean. Given that the population standard deviation (σ) is 12, use appropriate technology to calculate the required sample size. Determine if this sample size is reasonable for real-world application. **Task:** 1. **Calculate the Required Sample Size:** - Formula: \[\text{Sample size} = \left(\frac{Z \times \sigma}{E}\right)^2\] - Where \(Z\) is the Z-score corresponding to the required confidence level (99%), \(\sigma\) is the standard deviation (12), and \(E\) is the desired margin of error (7). 2. **Assessment:** - Indicate whether the calculated sample size is a reasonable number of students to sample. **Options:** - Yes. This number of IQ test scores is a fairly large number. - No. This number of IQ test scores is a fairly large number. - Yes. This number of IQ test scores is a fairly small number. - No. This number of IQ test scores is a fairly small number. **Instructions:** - Enter the required sample size in the provided field, rounding up to the nearest integer. - Assess the reasonableness of the sample size by selecting the appropriate option.
Transcribed Image Text:**Title: Determining Sample Size for Estimating Mean IQ Scores** **Introduction:** An IQ test is designed such that the mean is 100 and the standard deviation is 12 for the population of normal adults. This task involves finding the sample size necessary to estimate the mean IQ score of statistics students with 99% confidence that the sample mean is within 7 IQ points of the true mean. Given that the population standard deviation (σ) is 12, use appropriate technology to calculate the required sample size. Determine if this sample size is reasonable for real-world application. **Task:** 1. **Calculate the Required Sample Size:** - Formula: \[\text{Sample size} = \left(\frac{Z \times \sigma}{E}\right)^2\] - Where \(Z\) is the Z-score corresponding to the required confidence level (99%), \(\sigma\) is the standard deviation (12), and \(E\) is the desired margin of error (7). 2. **Assessment:** - Indicate whether the calculated sample size is a reasonable number of students to sample. **Options:** - Yes. This number of IQ test scores is a fairly large number. - No. This number of IQ test scores is a fairly large number. - Yes. This number of IQ test scores is a fairly small number. - No. This number of IQ test scores is a fairly small number. **Instructions:** - Enter the required sample size in the provided field, rounding up to the nearest integer. - Assess the reasonableness of the sample size by selecting the appropriate option.
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