 # Standard Deviation and Standard Error (260 words)

Subject Mathematics General Statistics

## Question

In an essay of 250-275 words, thoroughly address the following items and respond to the related questions:

Define the term standard deviation. 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?
Hypothesis testing allows researchers to use sample data, taken from a larger population, to draw inferences (i.e., conclusions) about the population from which the sample came. Hypothesis testing is one of the most commonly used inferential procedures. Define and thoroughly explain the terms null hypothesis and alternative hypothesis. How are they used in hypothesis testing?

Define 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 4 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.

## Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

A particularly important distribution is the normal distribution characterized mean and standard deviation and is obeyed by large enough sample averages. Suppose we have a normal distribution with mean M=40, standard deviation s=5, and a measurement of...

This is only a preview of the solution. Please use the purchase button to see the entire solution

## Related Homework Solutions

Regression Analysis & Histograms \$13.00
Statistics
Regression
Histograms
Interpreting Data
Mathematics
Functions
Analysis
Tools
Options
Midpoints
Min Values
Max Values
Frequency
Graphs
Statistics Questions \$50.00
Mathematics
Statistics
General Statistics
Mean
Average
Normal Distribution
Standard Deviation
Probability
Least Squares in Multiple Regressions \$100.00
Mathematics
Statistics
Least Squares
Multiple Regressions
Hypothesis Testing
Predictor Variables
Sum of Squares
Residual Plots
Minitab
Partial F Test
Applied Statistics \$73.00
Companies
Statistics
Mathematics
Sales
Dataset
Variables
Analysis
Distribution
Visual Tools
Multiple Regression
Functions
Decisions
Statistics Problem: Agriculture Department \$8.00
Statistics
Mathematics
Agriculture Department
Average Coffee Consumption
Gallons
Random Sample
Standard Deviation
Normal Distribution
Percentage
Test Statistics
Alternative Hypothesis
Rejected Regions
Variables
Live Chats