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ECON 2110

Dr. Martin Gritsch

Assignment 7

A reminder about Academic Integrity from the syllabus:

Cheating in its various forms will be severely punished. The minimum penalty is a grade of zero on the assignment in question, but it can go up to expulsion from the university. If you have not done so yet, please familiarize yourself with the “Academic Integrity Policy” (available online at http://www.wpunj.edu/dotAsset/230122.pdf). All parts of that Policy are relevant and important, but for the online setting of the class, I especially would like to stress sections II.B. (on plagiarism) and II.C. (on collusion).

Please make sure that you truly understand what all parts of the policy mean. To name a few examples, working together with another student on an assignment, getting help on an assignment from someone else (e.g., a tutor), and copying another student’s work are all violations of the Academic Integrity Policy.

Please note that you have a choice with this assignment.

You can either answer the questions on page 2 or those on page 3. Please note that you need to make a choice which questions you will answer, i.e., you cannot turn in answers to both sets of questions for credit.

If you will answer the questions on page 3, please do not answer the questions on this page.

Question A1 (3 points)

Part (a) (1 point)

Suppose that you roll a die 36 times with the following outcomes:

Outcome	Frequency
1	10
2	2
3	3
4	8
5	4
6	9
Sum	36

At a significance level of 0.05, can we reject the null hypothesis that the die is fair (i.e., that all six outcomes occur equally often)?

Part (b) (1 point)

Suppose that you now roll the same die 360 times with the following outcomes:

Outcome	Frequency
1	100
2	20
3	30
4	80
5	40
6	90
Sum	360

At a significance level of 0.05, can we reject the null hypothesis that the die is fair (i.e., that all six outcomes occur equally often)?

Part (c) (0.5 points) What do you observe when you compare your results from parts (a) and (b)?

Part (d) (0.5 points)

Please provide an explanation for what you observed in part (c).

Question A2 (2 points) Suppose that in bags of Christmas M&Ms, half of the M&Ms are supposed to be red, and the other half green. In a bag with 120 M&Ms and using a significance level alpha of 0.05, what is the lowest number of green M&M’s at which we would not reject the null hypothesis that the proportions between the two colors are indeed equal in the population?

If you answered the questions on page 2, please do not answer the questions on this page.

Question B1 (3 points)

Suppose that 14 individuals take a two-day course that is supposed to improve their knowledge of Web page design, which is rated as “not proficient,” “proficient,” or “advanced proficient.” Of the 14 individuals in the sample, 12 are rated higher after the course than before, 1 individual is rated lower, and 1 individual’s assessment is unchanged. Using a significance level of 0.05, can we conclude from this information that the course is successful in improving individuals’ knowledge of Web page design?

Question B2 (2 points) Suppose that we have ratings of a restaurant from a sample of 54 customers. Each of the ratings is either “excellent,” “very good,” “good,” “fair,“ or “poor.” In order to test whether the typical rating is “good,” would you prefer a hypothesis test for the population mean (like in Chapter 10) or a hypothesis test for the population median (like in Chapter 18)? Justify your answer.

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