Standard Deviation, Hypotheses, and Standard Error
1. Define the term standard deviation. Why is it important to know the standard deviation for agiven sample? What do researchers learn about a normal distribution from knowledge of thestandard 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?
2. Hypothesis testing allows researchers to use sample data, taken from a larger population, todraw inferences (i.e., conclusions) about the population from which the sample came. Hypothesistesting is one of the most commonly used inferential procedures. Define and thoroughly explainthe terms null hypothesis and alternative hypothesis. How are they used in hypothesis testing?
3. Define the term standard error. Why is the standard error important in research using sampledistributions? Consider the following scenario: A random sample obtained from a population hasa mean of μ=100 and a standard deviation of σ = 20. The error between the sample mean and thepopulation mean for a sample of n = 16 is 5 points and the error between a sample men andpopulation mean for a sample of n = 100 is 2 points. Explain the difference in the standard errorfor the two samples.