# Mathematics

**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.

**33.**

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, which test would be used to properly analyze the data in this experiment?

[removed]A) *χ*^{2} test for differences between two proportions (related samples)

[removed]B) *χ*^{2} test for the differences among more than two proportions

[removed]C) *χ*^{2} test for differences between two proportions (independent samples)

[removed]D) *χ*^{2} test of independence

**34.** A local real estate appraiser analyzed the sales prices of homes in 2 neighborhoods to the corresponding appraised values of the homes. The goal of the analysis was to compare the distribution of sale-to-appraised ratios from homes in the 2 neighborhoods. Random and independent samples were selected from the 2 neighborhoods from last year’s homes sales, 8 from each of the 2 neighborhoods. Identify the nonparametric method that would be used to analyze the data.

[removed]A) the Wilcoxon Signed-Ranks Test, using the test statistic *W*

[removed]B) the Wilcoxon Rank Sum Test, using the test statistic *T*_{1}

[removed]C) the Wilcoxon Rank Sum Test, using the test statistic *Z*

[removed]D) the Wilcoxon Signed-Ranks Test, using the test statistic *Z*

**35.** TABLE 13-2

A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:

Referring to Table 13-2, what is the standard error of the estimate, *S*_{YX}, for the data?

[removed]A) 0.784

[removed]B) 16.299

[removed]C) 12.650

[removed]D) 0.885

**36.** TABLE 13-11

A company that has the distribution rights to home video sales of previously released movies would like to use the box office gross (in millions of dollars) to estimate the number of units (in thousands of units) that it can expect to sell. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different movie titles:

ANOVA

Referring to Table 13-11, which of the following assumptions appears to have been violated?

[removed]A) independence of errors

[removed]B) normality of error

[removed]C) homoscedasticity

[removed]D) none of the above