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pH in Rain An environmentalist wanted to determine if the mean acidity of rain differed among Alaska, Florida, and Texas. He randomly selected six rain dates at each of the three locations and obtained the following data:

(a) State the null and alternative hypotheses.

(b) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from a normal population.

(c) Test the hypothesis that the mean pHs in the rainwater are the same at the  level of significance.

(d) Draw boxplots of the pH in rain for the three states to support the results obtained in part (c).

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Putting It Together: Women, Aspirin, and Heart Attacks In a famous study by the Physicians Health Study Group from Harvard University from the late 1980s, 22,000 healthy male physicians were randomly divided into two groups; half the physicians took aspirin every other day, and the others were given a placebo. Of the physicians in the aspirin group, 104 heart attacks occurred; of the physicians in the placebo group, 189 heart attacks occurred. The results were statistically significant, which led to the advice that males should take an aspirin every other day in the interest of reducing the chance of having a heart attack. Does the same advice apply to women?
In a randomized, placebo-controlled study, 39,876 healthy women 45 years of age or older were randomly divided into two groups. The women in group 1 received 100 mg of aspirin every other day; the women in group 2 received a placebo every other day. The women were monitored for 10 years to determine if they experienced a cardiovascular event (such as heart attack or stroke). Of the 19,934 in the aspirin group, 477 experienced a heart attack. Of the 19,942 women in the placebo group, 522 experienced a heart attack.

(a) What is the population being studied? What is the sample?

(b) What is the response variable? Is it qualitative or quantitative?

(c) What are the treatments? (d) What type of experimental design is this?

(e) How does randomization deal with the explanatory variables that were not controlled in the study?

(f) Determine whether the proportion of cardiovascular events in each treatment group is different using a two-sample Z-test for comparing two proportions. Use the  level of significance. What is the test statistic?

(g) Determine whether the proportion of cardiovascular events in each treatment group is different using a chi-square test for homogeneity of proportions. Use the  level of significance. What is the test statistic?

(h) Square the test statistic from part (f) and compare it to the test statistic from part (g). What do you conclude?

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Suppose firms’ marginal and average costs are constant and equal to C, and that the inverse demand curve is given by P= a-bQ, where a, b, > 0.

A) Calculate profit maximizing Q if firms are perfect competitors. B) Calculate profit maximizing Q if the market is served by a monopolist.

C) Calculate Nash Equillibrium quantities for Cournot duopolists. What is the market output?

D) Calculate Nash Equillibrium quantities for Bertrand duopolists. What is the market output?

E) Suppose now there are n identical firms in a Cournot model. Compute the Nash equillibrum quantities as a function of n. Also compute market output?

F) Show that monopoly outcome can be reproduced by setting n = 1 in (E); that the Cournot duopoly can be reproduced by setting n = 2 in (E) and that the Bertrand duopoly can be reproduced by letting n →” role=”presentation” style=”display: inline-block; line-height: 0; font-size: 16.94px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;”>?? INF.

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2.

Your company has recently appointed Encik Rahman to replace Encik Zainuddin, who quit as the project manager due to personal conflicts with some of your colleagues. Both of them possess different leadership styles.
(a)

Due to problems faced by your company recently, many of your colleagues were not focused on their jobs. Suggest what Encik Rahman can do to get them to focus on their daily tasks.

( 10 )
(b) As many projects have not progressed well, Encik Rahman needs to revamp the project teams and delegate work. Explain the reasons for him to delegate work to his subordinates and TWO ways of doing it effectively.

( 10 )

( Total / Jumlah: 20 )
Syarikat anda telah melantik Encik Rahman untuk menggantikan Encik Zainuddin yang sudah berhenti kerja sebagai seorang pengurus projek disebabkan oleh konflik peribadi dengan beberapa rakan sekerja anda. Kedua-dua mereka mempunyai cara gaya memimpin yang berbeza.
(a)

Disebabkan oleh masalah yang timbul sejak kebelakangan ini, ramai di antara rakan sekerja anda tidak dapat memberi tumpuan kepada kerja-kerja mereka. Cadangkan apa yang Encik Rahman boleh lakukan untuk mengembalikan tumpuan mereka kepada kerja harian mereka.
(b) Memandangkan banyak projek tidak menunjukkan kemajuan, Encik Rahman perlu membuat penstrukturan semula pasukan projek dan melakukan delegasi kerja. Terangkan sebab-sebab dia perlu melakukan delegasi kerja dan DUA cara yang efektif untuk menjalankannya.

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