(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 c places.) Standard Error 8.00 (a) o = 32, n = 4 (b) o = 32, n = 16 (c) o = 32, n = 64 0.02 (b) What happens to the standard error each time you quadruple the sample size? The standard error is reduced by half.
(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 c places.) Standard Error 8.00 (a) o = 32, n = 4 (b) o = 32, n = 16 (c) o = 32, n = 64 0.02 (b) What happens to the standard error each time you quadruple the sample size? The standard error is reduced by half.
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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Transcribed Image Text:**Finding the Standard Error of the Mean**
**Objective:** To understand how the standard error of the mean changes based on different sample sizes.
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**Problem:**
(a) Calculate the standard error of the mean for each sampling situation (assuming a normal population). Round your answers to 2 decimal places.
- Given:
- σ (standard deviation) = 32
- Sample Situations:
- (i) n = 4, Standard Error = 8.00
- (ii) n = 16, Standard Error = 4.00
- (iii) n = 64, Standard Error = 2.00
**Graph/Diagram Explanation:**
The table indicates the standard error calculations for different sample sizes. It shows that as the sample size (n) increases, the standard error decreases. This illustrates the inverse relationship between sample size and standard error.
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(b) What happens to the standard error each time you quadruple the sample size?
- The standard error is reduced by half.
---
**Conclusion:**
Increasing the sample size decreases the standard error of the mean, which reflects more precise estimates of the population mean. Quadrupling the sample size results in the halving of the standard error, demonstrating the value of larger samples in statistical analysis.
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