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Please disregard part 2 of the assignment.

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ECON 301: Take-Home Assignment 3

Due Oct 25

General Instructions: You must work out your own answers to the assignments. If you have difficulties

with a question, you may consult others students and instructor for clues but not the full answers. It is

important for you to recognize the nature of the difficulty so that it can be remedied before its too late.

Instructions for this assignment: Every student needs to complete BOTH parts of this assignment.

Please turn in your assignment before the lecture starts on the due date.

PART I Hypothesis Testing

1. A professional rock climber claims that he can climb a particular mountain within half an hour. From

a random sample of 20 attempts, the rock climber averaged 33.3 minutes with a standard deviation of 3.9

minutes. Is there sufficient evidence to suggest that the climbers claim is incorrect at a significance level of

10 percent?

2. A professor of statistics wants to test that the average amount of money a typical college student spends

per day during spring break is $70. Based upon previous research, the population standard deviation is

estimated to be $17.32. The professor surveys 35 students and finds that the mean spending is $72.43.

Assume the significance level is 2%.

(a) What are the null and alternative hypotheses?

(b) Please use the confidence interval approach to test the null.

(c) Please use the critical value approach to test the null.

(d) Please use the p-value approach to test the null.

3. A company that receives shipments of batteries tests a random sample of nine of them before agreeing

to take a shipment. The company is concerned that the true mean lifetime for all batteries in the shipment

should be at least 50 hours. From past experience it is safe to conclude that the population distribution of

lifetimes is normal with a standard deviation of 3 hours. For one particular shipment the mean lifetime for

a sample of nine batteries was 48.2 hours. Test, at the 10% level, the null hypothesis that the population

mean lifetime is at least 50 hours.

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PART II Research Proposal

1. Please write down your group members names.

2. Please write down the specific question you are going to answer.

3. Please write down why you and your group members are interested in this question.

3. Please write a paragraph describing how you plan to answer the question. In the paragraph, you should

mention what data you plan to use, where you can get the data, how you plan to use the data and what

results you expect to find.

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Explanation & Answer:

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hypothesis testing

significance level

confidence interval

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