# MATHEMATICS

1. TABLE 11-3

A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.

A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7

Interpret the results of the analysis summarized in the following table:

MA

Referring to Table 11-3, the among-group degrees of freedom is

[removed]A) 3.
[removed]B) 4.
[removed]C) 16.
[removed]D) 12.

2. TABLE 11-3

A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.

A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7

Interpret the results of the analysis summarized in the following table:

Referring to Table 11-3, the within-group sum of squares is

[removed]A) 1.0606.
[removed]B) 4.3644.
[removed]C) 1.1825.
[removed]D) 3.1819.

3. A completely randomized design

[removed]A) has one factor and one block and multiple values.
[removed]B) can have more than one factor, each with several treatment groups.
[removed]C) has one factor and one block.
[removed]D) has only one factor with several treatment groups.

4. The F test statistic in a one-way ANOVA is

[removed]A) MSA/MSW.
[removed]B) SSA/SSW.
[removed]C) MSW/MSA.
[removed]D) SSW/SSA.

5. TABLE 11-2

An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers, on the average, as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output:

ANOVA

Referring to Table 11-2, the within groups degrees of freedom is

[removed]A) 19.
[removed]B) 16.
[removed]C) 4.
[removed]D) 3.

6. TABLE 11-5

A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties – General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) – and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. The president theorizes that foreign graduates will have higher mean charges than USA graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table.

Referring to Table 11-5, what assumption(s) need(s) to be made in order to conduct the test for differences between the mean charges of foreign and USA medical school graduates?

[removed]A) The charges in each group of doctors sampled are drawn from normally distributed populations.
[removed]B) The charges in each group of doctors sampled are drawn from populations with equal variances.
[removed]C) There is no significant interaction effect between the area of primary specialty and the medical school on the doctors’ mean charges.
[removed]D) All of the above are necessary assumptions.

7. TABLE 12-2

Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.

Referring to Table 12-2, at 5% level of significance, the critical value of the test statistic is:

[removed]A) 3.8415
[removed]B) 13.2767
[removed]C) 5.9914
[removed]D) 9.4877

8. TABLE 12-18

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows.

Referring to Table 12-18, the null hypothesis for the Friedman rank test is

[removed]A) H0: MField1 = MField2 = MField3 = MField4 = MField5
[removed]B) H0: MSmith = MWalsh = MTrevor
[removed]C) H0: μField1 = μField2 = μField3 = μField4 = μField5
[removed]D) H0: μSmith = μWalsh = μTrevor

9. TABLE 12-10

Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.

Average time spent reading story books

 Average time spent watching TV Less than 1 hour Between 1 and 2 hours More than 2 hours Less than 2 hours 90 85 130 More than 2 hours 655 32 8

Referring to Table 12-10, we want to test whether there is any relationship between average time spent watching TV and average time spent reading storybooks. Suppose the value of the test statistic was 164 (which is not the correct answer) and the critical value was 19.00 (which is not the correct answer), then we could conclude that

[removed]A) there is no connection between time spent reading storybooks and time spent watching TV.
[removed]B) there is connection between time spent reading storybooks and time spent watching TV.
[removed]C) more time spent watching TV leads to less time spent reading storybooks.
[removed]D) more time spent reading storybooks leads to less time spent watching TV.

10. TABLE 12-3

A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day’s transactions gave the counts shown in the table for each of the 5 memory locations, along with the number of reported errors.

The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

Referring to Table 12-3, the critical value of the test statistic at 1% level of significance is:

[removed]A) 13.2767
[removed]B) 7.7794
[removed]C) 23.2093
[removed]D) 20.0902

11. When testing for independence in a contingency table with 3 rows and 4 columns, there are ________ degrees of freedom.

[removed]A) 12
[removed]B) 5
[removed]C) 7
[removed]D) 6

12. TABLE 13-1

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges (Y)—measured in dollars per month—for services rendered to local companies. One independent variable used to predict the service charge to a company is the company’s sales revenue (X)—measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit the model:

E(Y) = β0 + β1X

The results of the simple linear regression are provided below.

= -2,700 + 20X, SYX = 65, two-tailed p value = 0.034 (for testing β1)

Referring to Table 13-1, interpret the estimate of σ, the standard deviation of the random error term (standard error of the estimate) in the model.

[removed]A) For every \$1 million increase in sales revenue, we expect a service charge to increase \$65.
[removed]B) About 95% of the observed service charges equal their corresponding predicted values.
[removed]C) About 95% of the observed service charges fall within \$130 of the least squares line.
[removed]D) About 95% of the observed service charges fall within \$65 of the least squares line.

13. In a simple linear regression problem, r and b1

[removed]A) must have opposite signs.
[removed]B) may have opposite signs.
[removed]C) must have the same sign.
[removed]D) are equal.

14. The sample correlation coefficient between X and Y is 0.375. It has been found that the p-value is 0.256 when testing H0 : ρ = 0 against the two-sided alternative H1 : ρ ≠ 0. To test H0 : ρ = 0 against the one-sided alternative H1 : ρ < 0 at a significance level of 0.2, the p-value is:

[removed]A) 0.256/2
[removed]B) 1 – 0.256/2
[removed]C) (0.256)2
[removed]D) 1 – 0.256

15. Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals – 0.30,

[removed]A) the slope (b1) is negative.
[removed]B) variable X is larger than variable Y.
[removed]C) there is no correlation.
[removed]D) the variance of X is negative.

16. In a multiple regression model, the adjusted r2

[removed]A) cannot be negative.
[removed]B) has to fall between 0 and +1.
[removed]C) can sometimes be greater than +1.
[removed]D) can sometimes be negative.

17. TABLE 14-5

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.

SUMMARY OUTPUT

ANOVA

Referring to Table 14-5, what fraction of the variability in sales is explained by spending on capital and wages?

[removed]A) 68.9%
[removed]B) 50.9%
[removed]C) 83.0%
[removed]D) 27.0%

18. TABLE 14-1

A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following:

Referring to Table 14-1, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be?

[removed]A) 60.88
[removed]B) 79.09
[removed]C) 17.98
[removed]D) 55.62

19. To explain personal consumption (CONS) measured in dollars, data is collected for

A regression analysis was performed with CONS as the dependent variable and ln(CRDTLIM), ln(APR), ln(ADVT), and SEX as the independent variables. The estimated model was

= 2.28 – 0.29 ln(CRDTLIM) + 5.77 ln(APR) + 2.35 ln(ADVT) + 0.39 SEX

What is the correct interpretation for the estimated coefficient for SEX?

[removed]A) Holding everything else fixed, personal consumption for females is estimated to be 0.39% higher than males on the average.
[removed]B) Holding everything else fixed, personal consumption for males is estimated to be 0.39% higher than females on the average.
[removed]C) Holding everything else fixed, personal consumption for females is estimated to be \$0.39 higher than males on the average.
[removed]D) Holding everything else fixed, personal consumption for males is estimated to be \$0.39 higher than females on the average.

20. The logarithm transformation can be used

[removed]A) to overcome violations of the homoscedasticity assumption.
[removed]B) to test for possible violations of the homoscedasticity assumption.
[removed]C) to overcome violations of the autocorrelation assumption.
[removed]D) to test for possible violations of the autocorrelation assumption.

21. Which of the following is NOT used to determine observations that have an influential effect on the fitted model?

[removed]A) the hat matrix elements hi
[removed]B) the Cp statistic
[removed]C) the Studentized deleted residuals ti
[removed]D) Cook’s distance statistic

22. TABLE 15-2

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they will gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β0 + β1X + β2X2 + ε
where Y = demand (in thousands) and X = retail price per carat.

This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:

SUMMARY OUTPUT

ANOVA

Referring to Table 15-2, what is the value of the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?

[removed]A) -5.14
[removed]B) 373
[removed]C) 0.95
[removed]D) none of the above

23. After estimating a trend model for annual time-series data, you obtain the following residual plot against time:

The problem with your model is that

[removed]A) the irregular component has not been accounted for.
[removed]B) the trend component has not been accounted for.
[removed]C) the cyclical component has not been accounted for.
[removed]D) the seasonal component has not been accounted for,

24.

TABLE 16-4

Given below are Excel outputs for various estimated autoregressive models for Coca-Cola’s real operating revenues (in billions of dollars) from 1975 to 1998. From the data, we also know that the real operating revenues for 1996, 1997, and 1998 are 11.7909, 11.7757 and 11.5537, respectively.

AR(1) Model:

AR(2)Model:

AR(3) Model:

Referring to Table 16-4, if one decides to use AR(3), what will the predicted real operating revenue for Coca-Cola be in 2001?

[removed]A) \$11.68 billion
[removed]B) \$11.59 billion
[removed]C) \$12.47 billion
[removed]D) \$11.84 billion

25.TABLE 16-3

The following table contains the number of complaints received in a department store for the first 6 months of last year.

Referring to Table 16-3, suppose the last two smoothed values are 81 and 96. (Note: they are not.) What would you forecast as the value of the time series for September?

[removed]A) 96
[removed]B) 81
[removed]C) 91
[removed]D) 86

26. A tabular presentation that shows the outcome for each decision alternative under the various states of nature is called:

[removed]A) a payback period matrix.
[removed]B) a decision tree.
[removed]C) a payoff table.
[removed]D) a decision matrix.

27. Blossom’s Flowers purchases roses for sale for Valentine’s Day. The roses are purchased for \$10 a dozen and are sold for \$20 a dozen. Any roses not sold on Valentine’s Day can be sold for \$5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine’s Day: 100, 200, or 400 dozen roses. If the probability of selling 100 dozen roses is 0.2 and 200 dozen roses is 0.5, then the probability of selling 400 dozen roses is

[removed]A) 0.7
[removed]B) 0.5
[removed]C) 0.2
[removed]D) 0.3

28. TABLE 17-2

The following payoff matrix is given in dollars.

Suppose the probability of Event 1 is 0.5 and Event 2 is 0.5.

Referring to Table 17-2, the EVPI is

[removed]A) 600
[removed]B) 400
[removed]C) 0
[removed]D) 300

29. TABLE 18-1

A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the percentage of papers delivered on time for a 10-day period and construct a p chart to see whether the percentage is too erratic.

Referring to Table 18-1, which expression best characterizes the p chart?

[removed]A) increasing trend
[removed]B) cycles
[removed]C) in-control
[removed]D) individual outliers

30. One of the morals of the red bead experiment is

[removed]A) only management can change the system.
[removed]B) variation is part of the process.
[removed]C) it is the system that primarily determines performance.
[removed]D) all of the above

31. TABLE 11-5

A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties – General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) – and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. The president theorizes that foreign graduates will have higher mean charges than USA graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table.

Referring to Table 11-5, what degrees of freedom should be used to determine the critical value of the F ratio against which to test for differences in the mean charges for doctors among the four primary specialty areas?

[removed]A) numerator df = 1, denominator df = 159
[removed]B) numerator df = 3, denominator df = 152
[removed]C) numerator df = 3, denominator df = 159
[removed]D) numerator df = 1, denominator df = 152

32. Which of the following components in an ANOVA table are not additive?

[removed]A) degrees of freedom
[removed]B) sum of squares
[removed]C) mean squares
[removed]D) It is not possible to tell.

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