# Mathematics

5.12 You are trying to develop a strategy for

… investing in two different stocks. The anticipated

annual return for a $1,000 investment in each stock under

four different economic conditions has the following probability

distribution:

Returns

Probability Economic Condition Stock X Stock Y

0.1 Recession -100 50

0.3 Slow growth 0 150

0.3 Moderate growth 80 -20

0.3 Fast growth 150 100

Compute the

a. expected return for stock X and for stock Y.

b. standard deviation for stock X and for stock Y.

c. covariance of stock X and stock Y.

d. Would you invest in stock X or stock Y? Explain.

Question 5.13

Suppose that in Problem 5.12 you wanted to create a

portfolio that consists of stock X and stock Y. Compute the

portfolio expected return and portfolio risk for each of the

following percentages invested in stock X:

a.30%

b.50%

c.70%

d. On the basis of the results of (a) through (c), which portfolio

would you recommend? Explain

Statistics 106

Homework 7

Due : Feb. 24, 2016, In Class

19.31 Refer to Eye contact effect Problems 19.12 and 19.13.

a. Estimate µ21 with a 99 percent confidence interval. Interpret your interval estimate.

b. Estimate µ1. with a 99 percent confidence interval. Interpret your interval estimate.

c. Prepare a bar graph of the estimated factor B level means. What does this plot suggest about the factor B main effects?

d. Obtain confidence intervals for µ.1 and µ.2, each with a 99 percent confidence coefficient. Interpret your interval estimates.

e. Prepare a bar graph of the estimated factor A level means. What does this plot suggest about the factor A main effects?

f. Obtain confidence intervals for D1 = µ2. − µ1. and D2 = µ.2 − µ.1; use the Bonferroni procedure and a 95 percent family confidence coefficient. Summarize your findings. Are your findings consistent with those in parts (c) and (e)?

g. Is the Bonferroni procedure used in part (f) the most efficient one that could be used here? Explain. (Hint: Scheffe’s procedure is also applicable for those comparisons in part (f), so calculate S and compare it with B)

h. How many pairwise comparisons are there between treatment means? Construct Tukey’s confidence intervals for these pairwise comparisons at family-wise confidence coefficient 95%. Based on these intervals, which pairs of treatment means are significantly different from each other at level 0.05?

20.5 Brainstorming. A researcher investigated whether brainstorming is more effective for larger groups than for smaller ones by setting up four groups of agribusiness executives, the group sizes being two, three, four, and five, respectively. He also set up four groups of agribusiness scientists, the group sizes being the same as for the agribusiness executives. The researcher gave each group the same problem: ”How can Canada increase the value of its agricultural exports?” Each group was allowed 30 minutes to generate ideas. The variable of interest was the number or different ideas proposed by the group. The results, classified by type of group (factor A) and size of group (factor B), were:

Factor B (size of group) Factor A j = 1 j = 2 j = 3 j = 4

(type of group) Two Three Four Five i = 1 Agribusiness executives 18 22 31 32 i = 2 Agribusiness scientists 15 23 29 33

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Assume that no-interaction ANOVA model is appropriate.

a. Plot the data in the format of Figure 20.1 in the textbook (plot of the observations Yi j). Does it appear that interaction effects are present? Does it appear that factor A and factor B main effects are present? Discuss.

b. Conduct separate tests for type of group and size of group main effects. In each test, use level of significance α = .01 and state the alternatives, decision rule, and conclusion. What is the P-value for each test?

c. Obtain confidence intervals for D1 = µ.2 − µ.1, D2 = µ.3 − µ.2, and D3 = µ.4 − µ.3; use the Bonferroni procedure with a 95 percent family confidence coefficient. State your findings.

d. Is the Bonferroni procedure used in pan (c) the most efficient one here? Explain.

20.6 Refer to Brainstorming Problem 20.5. It is desired to estimate µ14. Obtain a point estimate of µ14.

20.7 Refer to Brainstorming Problem 20.5. Conduct the Tukey test for additivity; use α = .01. State the alternatives, decision rule, and conclusion. If the additive model is not appropriate, what might you do?

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