BA 301.01Chapter 4 Homework
Identify
1) Suppose we have a data set from a survey of university students. The variables and possible outcomes are:
• Gender:
o M (male)or
o F (female)
• Job:
o High demand (works at a job at least 20 hours per week)
o Low demand (works at a job less than 20 hours per week) or
o No demand (does not work at a job)
• Status:
o Full-time (carries a course load equal to full-time student status) or
o Part-time (carries a course lead less than full-time student status)
• Children
o Yes (has at least one or more dependent children at home)
o No (has no dependent children)
For the scenarios described below, identify the type of probability (marginal, joint, or conditional)and variable(s) involved. If a conditional probability, also state which variable is given.
a) The probability that a randomly selected student is both female and has full-time status.
b) The probability that a randomly selected male student has children.
c) From among those with children, I pick a student at random: the probability this student has full-time status.
d) The probability that a randomly selected student is male.
e) Suppose I pick a student at random: the probability this student is a part-time student and has a high-demand job.
f) Suppose I pick a student at random: the probability that student has part-time status.
2) Examine the data on worksheet Q2. Suppose I have an oil exploration firm and I have three possible locations to develop. The value of the reserves depends on the future price of oil, which is uncertain. The possible price ranges and the likelihood of their occurring are shown in the first two columns. For example, there is a 25% chance that oil will be between $120 and $150 per barrel in the future.
The value of the locations depends on the price of oil. As well, different extraction technologies will also affect the profitability of the locations. Columns C through E show the value of each location (in millions of dollars) depending on the future price of oil. For example, if oil plummets to less than $50 per barrel, location 2 would have a worth of negative$27 million but location 3 would have a worth of positive $5.7 million.
What would you calculate if you wanted to know the following?Don't actually do the calculations. You should be able to answer each question in one sentence.
a) What would you calculate to determine which location has the highest expected profit?
b) What would you calculate to determine which location is the riskiest?
c) What would you calculate to determine which two locations are best diversified?
Execute
3) Upon completion of their respective homework assignments, marketing majors and operations management majors at a state university enjoy hanging out at the local tavern in the evenings. The data in worksheet Q3 contains the distribution of number of hours spent by these students at the tavern in a typical week, along with typical cumulative grade-point averages (on a 4-point scale) for marketing and operations management students with common social habits.
Calculate the means and standard deviations of the grade-point averages of the two groups of students as well as the correlation between the two. Remember, you must consider the probabilities. Simply using the Excel functions =AVERAGE, =STDEV, or =CORREL will yield an incorrect answer.
4) A local beer producer sells two types of beer, a regular brand and a light brand with 30% fewer calories. The company wants to investigate the relationship between beer type preference and worker type. A total of 400 local workers are surveyed. The results are shown in worksheet Q4. They are classified as either blue-collar or white-collar and asked what type of beer they prefer to drink: regular, light, or neither (doesn't drink beer). Compute the following probabilities. Pivot tables are probably the best way to approach this problem.
a) Find the marginal probability that a randomly selected worker prefers regular beer.
b) Find the joint probability that a randomly selected worker is both white-collar and prefers light-beer.
c) Find the conditional probability that a randomly selected regular-beer drinker is a blue collar worker (in other words, given that I have a regular-beer drinker, what is the probability this regular-beer drinker is a blue-collar worker)?
d) Find the conditional probability that a randomly selected white-collar worker does not like to drink beer at all (in other words, given that I have a white-collar worker, what is the probability this white-collar worker does not like to drink beer)?
Interpret
5) Suppose I surveyed undergraduate students randomly across campus. The survey asks each student their gender and their school (BPA, HSS, Ed., and NSM). Marginal, joint, and conditional probabilities have been calculated and are shown in worksheet
Q5. Note that some probabilities are missing (the yellow cells). Answer the following questions.
a) If I pick a student at random, what is more likely: that the student will be in HSS or NSM?
b) If I pick a student at random, what is more likely: that the student will be a male in HSS or a female in BPA?
c) If I pick a female student at random, what is more likely: that she will be in BPA or Education?
d) Fill in the missing probabilities (just type the numbers in the yellow cells).
e) Are the two variables Gender and School dependent or independent? Explain your reasoning.
6) Based on the data shown in sheet Q6, a journalist notes the statistics highlighted in yellow and writes an article with the following headline: "More Women than Men Murdered on the Job." Is this an accurate statement? Why or why not?