### Variance of Sample MeansA certain type of thread is manufactured with a mean tensile strength of 71.8 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample mean changed when the sample size is:(a) Increased from 49 to 256?(b) Decreased from 196 to 64?---#### Calculations:**(a) The sample variance (σ²)**...changes from \( \frac{5.6^2}{49} \) for \( n = 49 \) to \( \frac{5.6^2}{256} \) for \( n = 256 \).(Type integers or decimals. Do not round.)**(b) The sample variance (σ²)**...changes from \( \frac{5.6^2}{196} \) for \( n = 196 \) to \( \frac{5.6^2}{64} \) for \( n = 64 \).(Type integers or decimals. Do not round.)---These calculations illustrate how the sample variance changes inversely with the sample size. As the sample size increases, the sample variance decreases, and vice versa. This is an essential concept in statistics, particularly when understanding the distribution of sample means.This example can help students visualize and calculate how changes in sample size affect the variance of sample means in practical applications.

A certain type of thread is manufactured with a mean tensile strength of 71.8 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample nean changed when the sample size is a) increased from 49 to 256? b) decreased from 196 to 64? a) The sample variance from Type integers or decimals. Do not round.) b) The sample variance from Type integers or decimals. Do not round.) for n = 49 to for n = 196 to for n=256. for n = 64.

A certain type of thread is manufactured with a mean tensile strength of 71.8 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample nean changed when the sample size is a) increased from 49 to 256? b) decreased from 196 to 64? a) The sample variance from Type integers or decimals. Do not round.) b) The sample variance from Type integers or decimals. Do not round.) for n = 49 to for n = 196 to for n=256. for n = 64.

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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There are four numbers in a data set. They are 5, 3, 7, and 11. a) What is the ∑∑ x2x2 b) What is the (∑x)2(∑x)2 c) The formula for the population variance, σ2σ2 is ∑x2−(∑x)2nn∑x2-(∑x)2nn Use parts a and b to help calculate the population variance. d. Now get the population standard deviation.

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