Assume that the sample is a simple random sample obtained from a normally distributed population of IQ scores of statistics professors. Use the table below to find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 40% of sigma. Is this sample size practical?a. The minimum sample size needed is To be 95% confident that \( s \) is within a certain percentage of the value of \( \sigma \), the sample size \( n \) should be at least:- For 1%: \( n = 19,205 \)- For 5%: \( n = 768 \)- For 10%: \( n = 192 \)- For 20%: \( n = 48 \)- For 30%: \( n = 21 \)- For 40%: \( n = 12 \)- For 50%: \( n = 8 \)To be 99% confident that \( s \) is within a certain percentage of the value of \( \sigma \), the sample size \( n \) should be at least:- For 1%: \( n = 33,218 \)- For 5%: \( n = 1,336 \)- For 10%: \( n = 336 \)- For 20%: \( n = 85 \)- For 30%: \( n = 38 \)- For 40%: \( n = 22 \)- For 50%: \( n = 14 \)

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Answered: Assume that the sample is a simple…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Assume that the sample is a simple random sample obtained from a normally distributed population of IQ scores of statistics professors. Use the table below to find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 40% of sigma. Is this sample size practical?

a. The minimum sample size needed is

To be 95% confident that \( s \) is within a certain percentage of the value of \( \sigma \), the sample size \( n \) should be at least:

- For 1%: \( n = 19,205 \)
- For 5%: \( n = 768 \)
- For 10%: \( n = 192 \)
- For 20%: \( n = 48 \)
- For 30%: \( n = 21 \)
- For 40%: \( n = 12 \)
- For 50%: \( n = 8 \)

To be 99% confident that \( s \) is within a certain percentage of the value of \( \sigma \), the sample size \( n \) should be at least:

- For 1%: \( n = 33,218 \)
- For 5%: \( n = 1,336 \)
- For 10%: \( n = 336 \)
- For 20%: \( n = 85 \)
- For 30%: \( n = 38 \)
- For 40%: \( n = 22 \)
- For 50%: \( n = 14 \)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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