# MATHEMATICS

7.

The data in the Excel spreadsheet linked below gives the average monthly price of gold (in dollars per ounce) for the years 1980 to1983.

Which of the following statistics measures gold price variation in the same units as gold price itself (i.e., dollars per ounce)?

The standard deviation.

The variance.

The coefficient of variation.

None of the above.

Price of Gold (in $ per ounce) |
|||||

Month | 1980 | 1981 | 1982 | 1983 | |

Jan | 675.30 | 557.38 | 384.38 | 481.29 | |

Feb | 665.32 | 499.76 | 374.13 | 491.96 | |

Mar | 553.58 | 498.76 | 330.04 | 419.70 | |

Apr | 517.41 | 495.80 | 350.34 | 432.93 | |

May | 513.82 | 479.69 | 333.82 | 438.08 | |

Jun | 600.71 | 464.76 | 314.98 | 412.84 | |

Jul | 644.28 | 409.28 | 338.97 | 422.72 | |

Aug | 627.14 | 410.15 | 364.23 | 416.24 | |

Sep | 673.62 | 443.58 | 435.76 | 411.80 | |

Oct | 661.14 | 437.75 | 422.15 | 393.58 | |

Nov | 623.46 | 413.36 | 414.91 | 381.66 | |

Dec | 594.92 | 410.09 | 444.30 | 389.36 |

9.

bizneznuz.com, an online business news agency, conducts a poll. Visitors to the site are invited to click on one of two buttons in order to register that they “agree” or “disagree” with the following statement: “Funding for space exploration should be left entirely to the private sector.”

If bizneznuz.com wants to accurately measure its online readership’s support for government-funded space exploration, this poll will deliver a biased and unrepresentative response because:

The pool of respondents is self-selected.

All respondents have internet access.

bizneznuz.com targets mainly the business community.

All of the above.

12.

The average height of American women is distributed normally, with a mean of 63.5 inches and a standard deviation of 2.5 inches.

Approximately what percentage of American women are taller than 58.5 inches, but shorter than 68.5 inches?

50%

68%

84%

95%

13.

The histogram below displays the distribution of income among households in the United States in 2001. Suppose a researcher takes a random sample of 60 households and calculates average household income in the sample. Suppose 99 other researchers conduct identical studies, each independently collecting a random sample of 60 households and computing the average household income in that sample.

Which of the following best describes the distribution of the 100 different average household incomes calculated by the researchers?

Symmetric with one peak.

Symmetric with two peaks.

Skewed left.

Skewed right.

21. In a survey of 48 citizens, 36 registered strong disapproval with their government’s economic leadership. In the previous month, the proportion of participants registering strong disapproval was 65%.

At the 95% confidence level and using a two-sided test, which of the following statements do these data support?

There is not sufficient evidence to indicate that the proportion of participants registering strong disapproval has changed.

The proportion of participants registering strong disapproval has increased.

The proportion of participants registering strong disapproval has stayed the same.

None of the above.

22.

A telemarketing company wants to find out if people are more likely to answer the phone between 8pm and 9pm than between 7pm and 8pm. Out of 96 calls between 7pm and 8pm, 72 were answered. Out of 105 calls between 8pm and 9pm, 90 were answered.

Using a one-sided hypothesis test with a 90% confidence level, which of the following statements do these data support?

There is not sufficient evidence that the proportion of people who answer the phone between 8pm and 9pm is greater than the proportion who answer the phone between 7pm and 8pm.

People are more likely to answer the phone between 8pm and 9pm.

Telemarketers should not call at all during the evenings.

People are more likely to answer the phone between 7pm and 8pm.

23.

The regression analysis below relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars.”

Which of the following is the lowest level at which the independent variable is significant?

0.94

0.10

0.05

0.01

24. The regression analysis below relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars.”

The coefficient on the independent variable tells us that:

For every additional trillion dollars of GDP, average energy consumption increased by 3,786 trillion BTUs.

For every additional dollar of GDP, average energy consumption increased by 3,786 trillion BTUs.

For every additional trillion dollars of GDP, average energy consumption increased by 3,786 BTUs.

For every additional trillion BTUs of energy consumption, average GDP increased by $3,786 trillion.

25.

The regression analysis below relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars.”

Which of the following statements is true?

The y-intercept of the regression line is 62,695 trillion BTUs.

The x-intercept of the regression line is $62,695 trillion.

In the event that a thermonuclear war completely halts all economic activity and the US GDP drops to zero, energy consumption will sink to 62,695 trillion BTUs.

None of the above.

26.

The regression analysis below relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars.”

In a given year, if GDP is $7.4 trillion, expected energy consumption is:

Around 90,711 trillion BTUs

Around 91,501 trillion BTUs

Around 28,016 trillion BTUs

Around 467,729 trillion BTUs.

27.

How much of the variation in energy consumption can be explained by variation in the gross domestic product?

About 94%

About 97%

About 99.99%

Almost none of the variation in energy consumption can be explained by variation in GDP.

30.

The data table below tabulates a pizza parlor’s advertising expenditures and sales for 8 consecutive quarters. The marketing manager wants to know how much of an impact current advertising will have on sales two quarters from now.

When running a regression with the dependent variable “sales” and the independent variable “advertising lagged by two quarters,” how many data points can she use, given the available data?

6

7

8

9

31.

In a regression analysis, a residual is defined as:

The difference between the actual value and the predicted value of the dependent variable.

The difference between the actual value and the predicted value of the independent variable.

The proportion of the variation in the independent variable that remains unexplained by the variation in the dependent variable.

The proportion of the variation in the dependent variable that remains unexplained by the variation in the independent variable.

32.

When comparing two regression analyses that have a different number of independent variables, which of the following should be used to compare the explanatory power of the two regressions?

Adjusted R-squared.

R-squared.

The correlation coefficient (“Multiple R”).

None of the above.

33.

Amalgamated Fruits, Vegetables, and Legumes, an agricultural company, breeds the experimental fruit “kiwana.” The company is studying the effects of a new fertilizer on the number of kiwanas per bunch grown on kiwana trees. The regression analysis below relates the number of kiwanas per bunch to the independent dummy variable “fertilizer.”

Based on the regression, which of the following statements may be concluded?

On average, the use of the new fertilizer increases the number of kiwanas per bunch by 5.25.

The independent dummy variable “fertilizer” is significant at the 0.01 level.

Variation in the independent dummy variable “fertilizer” explains around 53% of the variation in the number of kiwanas per bunch.

None of the above.

35.

Market researcher Ally Nathan is studying the relationships among price, type (classical or steel string), and consumer demand for acoustic guitars. She wants to find the relationship between demand and price, controlling for type.

To determine this relationship, she should:

Run a simple regression of the dependent variable demand on the independent variable price and observe the coefficient on price.

Run a simple regression of the dependent variable demand on the independent variable type and observe the coefficient on type.

Run a multiple regression of the dependent variable demand on the independent variables price and type and observe the coefficient on price.

Run a multiple regression of the dependent variable demand on the independent variables price and type and observe the coefficient on type.

36. The table below displays data on defect rates at a compact disk (CD) pressing facility. The table includes data on the distribution of CDs that have content errors (missing and/or wrong content), and on the distribution of CDs that have labeling errors.

What is the probability that a randomly selected CD has a content error?

1.00%

0.98%

0.02%

None of the above.