MATH 533 Final Exam (DEVRY)
Page 1
Question 1. 1. (TCO A) An insurance company researcher conducted a survey on the
number of car thefts in a large city for a period of 20 days last summer. The results are as
follows.
52
58
75
59
62
77
56
59
51
66
55
68
50
53
67
65
69
57
73
72
a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for
the above sample data on number of car thefts.
b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33)
2. (TCO B) Consider the following data on newly hired employees in relation to which part
of the country they were born and their highest degree attained.
HS
BS
MS
PHD
Total
East
3
5
2
1
11
Midwest
7
9
2
0
18
South
5
8
6
2
21
West
1
7
8
6
22
16
29
18
9
72
Total
If you choose one person at random, then find the probability that the person
a. is from the Midwest.
b. is from the South and has a PHD.
c. is from the West, given that person only holds a MS degree. (Points : 18)
3. (TCO B) A source in the Internal Revenue Service has stated that historically 90% of
federal tax returns filed are free of arithmetic errors. A random sample of 25 returns are
selected and checked carefully for arithmetic errors. Assuming independence, find the
probability that
a. all 25 returns are free of arithmetic errors.
b. at most 23 returns are free of arithmetic errors.
c. more than 17 are free of arithmetic errors. (Points : 18)
4. (TCO B) At a local supermarket the monthly customer expenditure follows a normal
distribution with a mean of $495 and a standard deviation of $121.
a. Find the probability that the monthly customer expenditure is less than $300 for a
randomly selected customer.
b. Find the probability that the monthly customer expenditure is between $300 and $600
for a randomly selected customer.
c. The management of a supermarket wants to adopt a new promotional policy giving a free
gift to every customer who spends more than a certain amount per month at this
supermarket. Management plans to give free gifts to the top 8% of its customers (in terms of
their expenditures). How much must a customer spend in a month to qualify for the free
gift? (Points : 18)
5. (TCO C) DJ Car Rental wants to estimate the average number of miles traveled per day by
each of its cars rented in California. A random sample of 110 cars rented in California yields
the following results.
Sample Size = 110
Sample Mean = 85.5 mi
Sample Standard Deviation = 19.3 mi
a. Construct the 99% confidence interval for the average number of miles traveled per day
by each of its cars rented in California.
b. Interpret this interval.
c. How many cars should be sampled if we wish to construct a 99% confidence interval for
the average number of miles traveled per day that is accurate to within 2 mi? (Points : 18)
6. (TCO C) A marketing research firm wishes to estimate the percentage of homeowners
who are dissatisfied with their present homeowner’s insurance policy. A simple random
sample of 400 homeowners led to 80 who were dissatisfied with their homeowner’s
insurance policy.
a. Compute the 95% confidence interval for the population percentage of homeowners who
are dissatisfied with their present homeowner’s insurance policy.
b. Interpret this confidence interval.
c. How many homeowners should be sampled in order to be 95% confident of being within
2% of the population percentage of homeowners who are dissatisfied with their present
homeowner’s insurance policy? (Points : 18)
7. (TCO D) A contract dispute between the National Football League and the Player’s Association arose regarding
the retirement system. The NFL agreed to a settlement only if it could be shown convincingly that less than 60% of
the players retired with 5 years or less playing time in their careers. A random sample of 200 retired NFL players is
selected with 116 having played for 5 years or less. Does the sample data provide evidence to conclude that the
percentage of players retiring with 5 years or less of playing time is less than 60% (using = .01)?
a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed pvalue for the hypothesis test and interpret this value. What does this mean?
h. Does this sample data provide evidence (with = .01), that the percentage of players retiring with 5 years or less
of playing time is less than 60%? (Points : 24)
8. (TCO D) A restaurant franchise company has a policy of opening new restaurants only in
areas that have a mean household income in excess of $65,000. The company is currently
considering an area to open a new restaurant. A random sample of 144 households from
this area is selected yielding the following results.
Sample Size = 144
Sample Mean = $66,124
Sample Standard Deviation = $7,400
Does the sample data provide evidence to conclude that the population mean annual
household income is in excess of $65,000 (using = .05)? Use the hypothesis testing
procedure outlined below.
a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection
regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What
does this mean?
h. Does the sample data provide evidence to conclude that the population mean annual
household income is in excess of $65,000 (using = .05)? (Points : 24)
Page 2
Question 1. 1. (TCO E) The Central Company manufactures a certain item once a week in a batch production run.
The number of items produced in each run varies from week to week as demand fluctuates. The company is
interested in the relationship between the size of the production run (SIZE, X) and the number of personhours of
labor (LABOR, Y). A random sample of 13 production runs is selected, yielding the data below.
SIZE
LABOR
PREDICT
40
83
60
30
60
100
70
138
90
180
50
97
60
118
70
140
40
75
80
159
70
140
40
75
80
159
70
144
50
90
60
125
50
87
Correlations: SIZE, LABOR
Pearson correlation of SIZE and LABOR = 0.990
PValue = 0.000
Regression Analysis: EMP. versus FLIGHTS
The regression equation is
LABOR = 6.16 + 2.07 SIZE
Predictor Coef SE Coef T P
Constant 6.155 5.297 1.16 0.270
SIZE 2.07371 0.08717 23.79 0.000
S = 5.20753 RSq = 98.1% RSq(adj) = 97.9%
Analysis of Variance
Source DF SS MS F P
Regression 1 15349 15349 565.99 0.000
Residual Error 11 298 27
Total 12 15647
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 118.27 1.45 (115.07, 121.46) (106.37, 130.17)
2 201.22 3.90 (192.64, 209.80) (186.90, 215.53)X
X denotes a point that is an extreme outlier in the predictors.
Values of Predictors for New Observations
New Obs SIZE
1 60
2 100
a. Analyze the above output to determine the regression equation.
b. Find and interpret β˖1in the context of this problem.
c. Find and interpret the coefficient of determination (rsquared).
d. Find and interpret coefficient of correlation.
e. Does the data provide significant evidence (= .05) that the size of the production run can be used to predict the
total labor hours? Test the utility of this model using a twotailed test. Find the observed pvalue and interpret.
f. Find the 95% confidence interval for the mean total labor hours for all occurrences of having production runs of
size 60. Interpret this interval.
g. Find the 95% prediction interval for the total labor hours for one occurrence of a production run of size 60.
Interpret this interval.
h. What can we say about the total labor hours when we had a production run of size 100? (Points : 48)
Page 3
1. (TCO E) At an auction, a national car rental agency sold 12 comparably equipped 3yearold Chevrolet Corsicas.
The data on mileage (X1), type of car (X2), and selling price (Y) are found below.
Y = PRICE ($)
X1= MILEAGE (miles)
X2= TYPE (dummy variable 0=sedan, 1=coupe)
The data is given below (in MINITAB).
PRICE
Mileage
Type
PredMile
PredType
7000
60000
0
54000
0
8500
52000
0
54000
1
7000
62000
0
8900
48000
0
7600
55000
0
7200
60000
1
8500
50000
1
7800
53000
1
7200
58000
1
9000
48000
1
7200
60000
1
7700
55000
0
Correlations: PRICE, Mileage, Type
PRICE Mileage
Mileage 0.970
0.000
Type 0.023 0.053
0.942 0.871
Cell Contents: Pearson correlation
PValue
Regression Analysis: PRICE versus Mileage, Type
The regression equation is
PRICE = 15841 0.146 Mileage 39 Type.
Predictor Coef SE Coef T P
Constant 15840.9 671.4 23.59 0.000
Mileage 0.14562 0.01205 12.09 0.000
Type 39.5 114.1 0.35 0.737
S = 197.278 RSq = 94.2% RSq(adj) = 92.9%
Analysis of Variance
Source DF SS MS F P
Regression 2 5689732 2844866 73.10 0.000
Residual Error 9 350268 38919
Total 11 6040000
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 7977.5 82.1 (7791.7, 8163.3) (7494.1, 8460.9)
2 7938.0 81.2 (7754.4, 8121.6) (7455.4, 8420.6)
Values of Predictors for New Observations
New Obs Mileage Type
1 54000 0.00
2 54000 1.00
a. Analyze the above output to determine the multiple regression equation.
b. Find and interpret the multiple index of determination (RSq).
c. Perform the ttests on β˖1, β˖2 (use two tailed test with (= .05). Interpret your results.
d. Predict the price for an individual Chevy Corsica with mileage of 54,000 miles and with type being sedan. Use
both a point estimate and the appropriate interval estimate. (Points : 31)