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# Statistics : Hypothesis Testing, Test Statistic and Critical Region

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1. Why do we use hypothesis testing?

2. What is a test statistic and how is it related to a critical value in hypothesis testing?

3. What is the critical region in hypothesis testing and why is it important?

##### Solution Summary

The following posting helps with various statistics problems. Hypothesis testing, test statistics and critical regions are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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In practice, when we study a population or two populations, there may exist many parameters such as the mean and the standard deviation which are unknown. So we have to estimate them. Once we got an estimation, we have to test if the true value is equal (or close to) this value.

When we test if the true value is equal (or close to) this value, the first step we need to do is to set up the null hypothesis and alternative hypothesis. Then we ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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