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# Hypothesis Testing And Central Limit Theorem

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(b) The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. She performs a two-tailed test of the null hypothesis that the mean for the stressed oak furniture is 650. What are Type I and Type II errors for this problem?

(c) A 95% confidence interval for is from -2 to 10. What conclusion can we make based on this confidence interval if we test Ho: µ = 0 against H1: µ ? 0 at = 0.05?

(d) What is the Central Limit Theorem? Why is it important in statistical data analysis? How is the rule of thumb used for the application of the Central Limit Theorem?

https://brainmass.com/statistics/central-limit-theorem/hypothesis-testing-and-central-limit-theorem-540791

#### Solution Preview

b) this is type one error. the women wants to test if the mean for the stressed oak furniture is 650, this is the concept of type I error.

c) we will fail to reject H0 because confidence ...

#### Solution Summary

The solution gives detailed steps on determining type I and type II errors in a specific hypothesis testing and using confidence interval method to make the conclusion of the same test. Next, central limit theorem is well defined and explained in details.

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## Central Limit Theorem and its implications in Hypothesis Testin

Q1: What do you remember from the CLT and it's implications? Please touch up on them.

Q2: Please explain how this theory is used in testing hypothesis.

Q3: What are confidence intervals telling us?

Q4: What region under the normal curve corresponds to Researcher's confidence?

Q5: What are the area under the 2 tails of normal curve used for, and what they tell us? How do we use them in hypothesis tests?

Q6: Who decides what the confidence level in a hypothesis test should be and based on what factors?

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