Download FINAL Fall 2012 Venable Statistics NAME_____________ Please

FINAL Fall 2012 Venable Statistics
NAME_____________
Please show all work – even work done by calculator.
Problems #1 – 4 are worth 20 points each, and problems #5 – 8 are worth 10 points each.
1. The pizza shop management claims that 40% of the orders received are for cheese
and sausage pizzas, 20% are for cheese and mushroom pizzas, 15% are for cheese
and green pepper pizzas, and 25% are for other kinds of pizzas. A record of 100
orders showed that 32 of them were for cheese and sausage pizzas, 24 were for
cheese and mushroom pizzas, 25 were for cheese and green pepper pizzas, and 19
were for other kinds of pizzas. Using the 5% significance level, test the null
hypothesis that the claim of the pizza shop management is true.
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2. A consumer agency wanted to investigate if four insurance companies differed
with regard to the premiums they charge for auto insurance. The agency
randomly selected a few auto drivers who were insured by each of these four
companies and had similar driving records, autos, and insurance policies. The
following table gives the premiums paid per month by these drivers insured with
these four insurance companies. Assume that all assumptions required to apply
the one-way ANOVA procedure hold true.
Company A
75
83
68
52
Company B
59
75
100
Company C
65
70
97
90
73
Company D
76
60
52
58
Using the 1% significance level, test the null hypothesis that the mean auto
insurance premium paid per month by all drivers insured by each of these four
companies is the same.
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3. Two drugs were administered to two groups of randomly assignment 60 and 40
patients, respectively, to cure the same disease. The following table gives
information about the number of patients who were cured and not cured by each
of the two drugs.
Drug I
Drug II
Cured
44
18
Not Cured
16
22
Test at the 1% significance level whether or not the two drugs are similar in
curing and not curing the patients.
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4. The following table lists the ages (in years) and the prices (in thousands of
dollars) for a sample of seven cars of the same model.
Age
Price
8
4.0
11
3.0
4
9.5
2
13.0
6
8.0
5
9.0
13
1.5
a. Construct a scatter diagram for these data. (Please see next page.)
b. Find the equation for the least squares regression line with advertising expenditure as an
independent variable and total sales as a dependent variable. Show your work and all
subtotals.
c. Graph the regression line.
d. Predict the price of a 7-year old car.
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5. The following give the rainfall in inches for a 7 days in a certain town.
Find the mean and the standard deviation.
3
2
2
0
4
1
1
2
6. The following are 16 scores from a midterm test.
64
78
93
66
89
93
97
61
52
100
93
96
92
91
66
100
a. Find the median.
b. Find the approximate value of the 75th percentile.
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7. Fifty two percent of a certain county’s adult residents are female. If an citizen’s
oversight committee is formed by choosing 12 adult county residents at random,
what is the probability that none of the committee members are female? Round
your answer to four decimal places.
8. A consumer agency that proposes that lawyers’ rates are too high wanted to
estimate the mean hourly rate for all lawyers in New York City. A sample of 70
lawyers taken from New York City showed that the mean hourly rate charged by
them is $420. The population standard deviation of hourly charges for all lawyers
in New York City is $110. Construct a 92% confidence interval for the mean
hourly charges for all lawyers in New York City.
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