# Discussion on Standard Deviation and Standard Error

Why is it important to know the standard deviation for a given sample? What do researchers learn about a normal distribution from knowledge of the standard deviation? A sample of n=20 has a mean of M = 40. If the standard deviation is s=5, would a score of X= 55 be considered an extreme value? Why or why not?

Can you please define and thoroughly explain the terms null hypothesis and alternative hypothesis. Can you expalin how are they used in hypothesis testing?

What is meant by the term standard error. Why is the standard error important in research using sample distributions?

Consider the following scenario: A random sample obtained from a population has a mean of µ=100 and a standard deviation of σ = 20. The error between the sample mean and the population mean for a sample of n = 16 is 5 points and the error between a sample men and population mean for a sample of n = 100 is 2 points. Explain the difference in the standard error for the two samples.

Please provide at least 2-3 scholarly research sources. May I suggest, Statistics for the Behavioral Sciences (9th) ed., by Gravetter & Wallnau (2010)? Thank you.

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#### Solution Preview

Why is it important to know the standard deviation for a given sample? What do researchers learn about a normal distribution from knowledge of the standard deviation? A sample of n=20 has a mean of M = 40. If the standard deviation is s=5, would a score of X= 55 be considered an extreme value? Why or why not?

Answer: standard deviation for a given sample is important because if standard deviation is large, the sample can not represent the population. researchers learn about a normal distribution from knowledge of the standard deviation as follows: 68% of population ...

#### Solution Summary

The solution gives detailed discussion on the concepts and applications of standard error and standard deviation and their roles in the hypothesis testing.

A Discussion of Sample Sizes

By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 4.5 seconds.

a. How many measurements should be made in order to be 95% certain that the maximum error of estimation will not exceed 1 second?

b. What sample size is required for a maximum error of 2 seconds?