## Question

Please read each question carefully and answer it completely. (Note that although you are not always required to “show work” on the homework assignments, you may be required to do so on exams.)

#1. In the EXCEL file you are given data taken from the World Bank’s “Doing Business” website. You will consider whether “the cost of enforcing contracts (as a % of the claim)” is the same across the three regions for which you have data.

(a) Please conduct a four-step ANOVA hypothesis test for the test described above, set α = 0.04. [Note that if you run this test in EXCEL you will want to re-format how the data is reported.]

(b) If appropriate based on your results from (a), please conduct post-hoc testing for pairwise comparisons as described as “Fisher’s LSD” in textbook section 13.3 [i.e. please use the procedure finding the specific LSD.] You do not need to conduct “four step hypothesis tests” for these comparisons, just please highlight which pairs reject the null hypothesis of no difference. Continue to use α = 0.04. When would such a post-hoc procedure not be appropriate with such an ANOVA model? [Hint: Be sure to first discuss specifically how the null hypothesis between the ANOVA F and the LSD tests differ. Then, feel free to go further and discuss other concerns researchers have about “post-hoc” tests in general.]

(c) Describe the issues of finding the appropriate Type I Error for your “post-hoc” results. How would you apply the appropriate Boneferroni correction to the tests you ran in (b)?

#2. Consider the information for #25 on p. 576. Note that you are provided this data in the EXCEL file/worksheet “midwestgas.” [question begins with “The price drivers pay for gasoline often varies …”]

(a) Please conduct a four-step ANOVA hypothesis test as described in the textbook question (i.e. that means are equal across brands, set α = 0.05.) IMPORTANT: If you run this test using the Data Analysis Toolpak in EXCEL, make sure you report the correct F-statistic as EXCEL will report two F-statistics. Make sure you read the instructions in Appendix 13.2 to be sure you select the correct command in EXCEL to correspond to the “randomized block design” and for examples from the textbook.

(b) Explain what the “blocks” are in this experiment and how they change the ANOVA model from a randomized/observational design such as described in textbook section 13.2.

#3. You are given the following pmf for X and Y:

X
0 1 2
0 0.05 0.10 0.03
Y 1 0.21 0.11 0.19
2 0.08 0.15 0.08

(a) The marginal pmfs for X and Y.
(b) E(X) and E(Y).
(c) The conditional distributions for (X|Y) “X given Y” and (Y|X) “Y given X.”
(d) E(Y|X) and Var(Y|X).

## Solution Preview

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SOLUTION #1
(a)
Step 1: Hypothesis:
Null Hypothesis:
H0: There is no significant difference in the means of Cost of Enforcement (% of claim) between the three regions i.e. ASIA, CENTRAL/S AMER and SUB SAH AFRICA i.e.μ1 = μ2 = μ3
Alternative Hypothesis:
HA: There is a significant difference in the means of Cost of Enforcement (% of claim) between the three regions i.e. means are not all equal
Step 2: Selection of the test statistic and decision rule
The test statistic is the F statistic for ANOVA, F=MSB/MSE
Reject H0 if calculated F value is greater than the critical value of F or if the p-value is less than the level of significance i.e. 0.04 then we will reject the null hypothesis as well....

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