MAR 5620 – Quiz 1 – Fall 2004
- A cable company’s marketing manager is interested in obtaining information regarding her company’s subscribers. She sends out a survey, and asks the respondent to fill in the following information. Give the best description of each variable (nominal, ordinal, numeric (interval) as received by the manager.
a)Number of people living in household Numeric
b)Household income (<20K.20-29.9K,30-39.9K,40-49.9K,>50K) Ordinal
c)Ever purchased a satellite dish? Nominal
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- A drug manufacturer is interested in testing the efficacy of a drug aimed at increasing birthweight of children born to women with a particular condition. They identify 200 women with the condition who are in the first term of pregnancy and randomize 100 to receive the test drug and 100 to receive the placebo. For each part, circle the best answer.
a)This is an observational study, survey, or controlled experiment
b)The women enrolled in the study are a sampleor population
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- An online DVD service selected a random sample of n=10 customers, and observed the number of DVD’s each ordered during the past 3 months (all have been members over the full period). Give a stem-and-leaf-plot, the sample mean, median, variance, and standard deviation.
# DVDs X-Xbar (X-Xbar)^2
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6 -19 361
26 1 1
38 13 169
12 -13 169
19 -6 36
29 4 16
8 -17 289
52 27 729 Median=(26+29)/2=27.5
31 6 36
29 4 16
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Sum=250 1822
Xbar=25 S^2=1822/(10-1)=202.4
S=14.2
- The following scatterplot gives a plot of firm costs (100,000s of pounds) versus car miles (millions) for a passenger bus firm in London over 20 time periods.
The means, standard deviations, and covariance are given below.
Variable / Mean / Std Dev / Covariance (with other var)Miles / 3.41 / 0.3891 / 0.0640
Cost / 2.17 / 0.1795 / 0.0640
a)Give the equation that is drawn on the plot.
b)Give estimates of the fixed costs (in 100,000s of pounds) and marginal cost of increasing miles by 1 million (in 100,000s of pounds)
Fixed Costs: 0.729
Marginal Costs: 0.423
- The following contingency table gives satisfaction ratings among customers for the two branches of a small town bank (1000 customers sampled from each branch).
Satisfied with Service / Branch A / Branch B / Total
Yes / 650 / 850 / 1500
No / 350 / 150 / 500
Total / 1000 / 1000 / 2000
a)If a customer is selected at random, what is the probability he/she is satisfied with the service?
1500/2000 = 0.75
b)If a customer is selected at random, what is the probability he/she is not satisfied with the service if at Branch A?
350/1000 = 0.35
c)Is service satisfaction independent of branch? Why?
N0 P(Sat | A) = 0.65 ≠ P(Sat | B) = 0.85 ≠ P(Sat) = 0.75
d)Given a customer is not satisfied, what is the probability he/she was served at Branch A?
P(A | Not Sat) = 350/500 = 0.70
- A financial analyst places the following probability distribution for the return (in dollars) in one year for a $100 investment in a firm. (Return=Year end value-$100).
Return Probability xp(x) x^2p(x)
-20 .20 -4 80
0 .20 0 0
20 .60 12 240
Sum mu=8 320 sigma^2=320-(8)^2=256
The following 3 Problems are based on this information
An appliance store owner has determined from historic records the following joint probability distribution for the number of stoves (rows) and refrigerators (columns) sold daily.
Stoves\Refrigerators / 0 / 1 / 20 / .12 / .13 / .10
1 / .09 / .18 / .13
2 / .09 / .14 / .02
7. Give the average number of stoves and refrigerators sold per day.
S p(s) sp(s) r p(r) rp(r)
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0 .35 0 0 .30 0
1 .40 .40 1 .45 .45
2 .25 .50 2 .25 .50
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sum .90 .95
- Give the covariance of the numbers of stoves and refrigerators sold per day.
- The firm makes a $100 profit on each stove sold and $200 profit on each refrigerator sold, what is their average daily profit?
.E(100S+200R)=100(.90)+200(.95)=90+190=$280/day
A cable company’s marketing manager is interested in obtaining information regarding her company’s subscribers. She sends out a survey, and asks the respondent to fill in the following information. Give the best description of each variable (nominal, ordinal, numeric (interval) as received by the manager.
a)Household annual income ($1000s) Numeric
b)Number of pay-pre-movies in past year (0,1-5,6-10,11-20,>21) Ordinal
c)Ever purchased a satellite dish? Nominal
A large national chain of restaurants is interested in comparing the profitability of its restaurants. They classify the individual extablishments as: urban, suburban, or rural road-side, and select 20 of each type, obtaining profit margins based on accounting records.
c)This is an observational study, survey, or controlled experiment
d)The restaurants measured in the study are a sampleor population
A cable company’s marketing manager is interested in obtaining information regarding her company’s subscribers. She sends out a survey, and asks the respondent to fill in the following information. Give the best description of each variable (nominal, ordinal, numeric (interval) as received by the manager.
d)Number of pay-per-view movies in past year Numeric
e)Quality of reception (Excellent, Good, Fair, Poor) Ordinal
f)Ever purchased a satellite dish? Nominal
A management professor is interested in business practices of large national manufacturing companies. He contacts purchasing manufacturers from all firms listed as manufacturing by the federal government and asks a series of questions regarding business practices. Circle the best answer for each part.
g)This is an observational study, survey, or controlled experiment
b) The firms measured in the study are a sample or population