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Homework #6 - Parameter Estimation and Hypothesis Testing

The fourth homework covers material in chapters 6 and 7.  The materials in those sections imply the following skills as being important: 

1. Concepts / Vocabulary:  Understand the concepts population, sample, estimator, parameter, point estimate, confidence interval, and sampling distribution of an estimator, statistical hypothesis, type I error, type II error, significance level, power, p value, and t distribution.
2. Estimators:  Identify and apply principles that guide the selection of estimators from a set of potential estimators.
3. Confidence Intervals:  Determine specified (1-alpha)% confidence intervals for a parameter, based on the properties of the sampling distribution of the parameter.
4. Hypothesis Testing - Single Parameters:  Define and conduct hypothesis tests concerning the true value of a single population parameter - the mean of a population, the variance, or the proportion of the population satisfying some criteria. 

Assignment

Key observations about the assignment: 
(a) Most of the problems are "odd" --> solutions are in the back of the book.  By being able to verify your answers when working the homework problems, you will not need to rely on the grading to determine correctness.   This seemed important since the test follows the submission of the homework by one day. 
(b) There are no additional problems.  However, there are additional thought questions.  I strongly encourage you to not only "think" about them but to try to answer them!

1.  Choosing an Estimator

7-1

Hint:  In working the problem, you should determine the expected value and variance of the two estimators suggested.   

2.  Sampling Distribution - Single Mean

7-24 and 7-25. 

Important but not required for submission:  Is the assumption of normality important in 7-24?  in 7-25?

3.  Sampling Distribution - Difference between two Means

7-31

4.  Hypothesis testing - General Ideas

8-7, 8-8, 8-9, 8-10:  These four problems are really all part of the same problem.  

5.  Hypothesis testing - Mean of Population, Variance Known

8-23

6.  Hypothesis testing - Mean of Population, Variance Unknown

8-31

7.  Hypothesis testing - Variance of a Population

8-41

8.  Hypothesis testing - Variance of a Population

8-47

Additionally, you should think about (but not submit) the following scenario:   Imagine that the manufacturer claims that less that 25% of its helmets sustain damage upon impact.  This data seems contrary to such a claim.  How might you use hypothesis testing to investigate your intuition.  What would be the null hypothesis and the alternate hypothesis?  What is the relationship between the rejection region for the hypothesis and the confidence interval in part

Questions and Answers

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Solutions

Solutions.