# Hypothesis Testing And Central Limit Theorem

(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?

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#### 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.