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Type I and Type II Error - Inferences about population

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Supposed you were interested in knowing the mean score for a certain quiz in a statistics class with 20 students. You sample four members of the class and find their scores to be 49, 56, 72, and 90. The professor reports that the mean was 72, but you are not sure that is correct. List the four possibilities and categorize the conclusions including the types of possible errors. Show all work

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Solution Summary

This post illustrates the four possibilities while we are making inferences about the population from the sample statistics. More precisely it discusses the type I and type II error in the context of hypothesis testing.

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1.

Sample Mean = (49+56+72+90)/4=66.75
Standard Deviation of Scores = ((49-66.75)^2+(56-66.75)^2+(72-66.75)^2+(90-66.75)^2)/3)^0.5=18.25
Standard Error = Standard Deviation / square root of sample size = 18.24/4^0.5 = 9.12
The observed value of t statistic is (66.75-72)/9.12 = -0.58
Depending upon the ...

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