A recent marketing survey related consumers’ awareness of a new marketing campaign with their rating of the product. A sample of consumers rated their awareness as “LOW” or “HIGH” and rated the product as “POOR” or “GOOD”. In the survey they found that P(POOR|LOW)=0.25, P(HIGH|POOR)=0.8, P(GOOD|LOW)=0.75 and P(HIGH|GOOD)=0.4. Fill in the below table and create a marginal and joint probability table. Explain your answer. [8%]
Awareness Low High Total Rating Poor 10 Good 10 Total 8 12
b) Firms are increasingly asking applicants to submit to drug tests. 10% of all applicants are drug users. Suppose that drug tests that are used to identify whether a randomly chosen person is a drug user or not are accurate only 98% of the time. What is the probability that a person who has tested positive for drug use is not really a drug user? Explain your answer using a tree diagram. [8%]
c) A publisher wishes to evaluate the effectiveness of a marketing campaign that promotes the adoption of his textbook in Higher Education. To do this, seventy five percent of all potential professors were reached in a focused advertising program. Twenty eight percent of those contacted adopted the textbook while eight percent of the adoptions came from professors who did not receive the promotional material. Use Bayes’ Theorem to find the probability that a professor who adopts the textbook received the advertising material. Explain your answer. [7%]
d) There are five men and four women working on a project. To handle one particular aspect of the project, a sub-committee needs to be formed. In the interest of balance, it is decided that the sub-committee will consist of two men and two women. How many combinations of this sub-committee are possible? [9%]
3 ECON1007 W1
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e) From past experience, it is known that 90% of babies can distinguish their mother’s voice from the voice of a similar sounding female. A random sample of 20 babies is given this voice recognition test. Find the probability that at least 4 babies do not recognize their mother’s voice. [8%]
f) It has been reported that 1.7% of the work force will retire this year. Consider a random sample of 200 workers. What is the probability that more than three of them will retire this year? Use the Poisson approximation to the Binomial Distribution. [8%]