# Define the term standard deviation

**Question description**

**General Requirements:**

Use the following information to ensure successful completion of the assignment:

- Read each segment of this assignment carefully. There is information in the segment that will guide your completion.
- Instructors will be using a grading rubric to grade the assignments. It is recommended that learners review the rubric prior to beginning the assignment in order to become familiar with the assignment criteria and expectations for successful completion of the assignment.
- Doctoral learners are required to use APA style for their writing assignments. The APA Style Guide is located in the Student Success Center.
- This assignment requires that at least two additional scholarly research sources related to this topic, and at least one in-text citation from each source be included.

**Directions:**

In an essay of 250-500 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 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.

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