# Mathematics

**1.**

The median is often a better representative of the central value of a data set when the data set:

Source

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·

Is bimodal.

·

Has a high standard deviation.

·

Is highly skewed.

·

Has no outliers.

2.

The data in the Excel spreadsheet linked below provide information on the nutritional content (in grams per serving) of some leading breakfast cereals.

For which nutrients is the mean nutrient content per serving greater than the median nutrient content per serving?

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Proteins only.

Complex carbohydrates only.

Both nutrients.

Neither nutrient.

3.

The histogram below plots the carbon monoxide (CO) emissions (in pounds/minute) of 40 different airplane models at take-off.

The distribution is best described as is:

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Uniform.

Heteroskedastic.

Normal.

Skewed right.

4.

The histogram below plots the carbon monoxide (CO) emissions (in pounds/minute) of 40 different airplane models at take-off.

Which of the following statements is the best inference that can be drawn from this histogram?

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The mean amount of carbon monoxide emissions is greater than the median amount of carbon monoxide emissions.

The mean amount of carbon monoxide emissions is less than the median amount of carbon monoxide emissions.

The mean and median amounts of carbon monoxide emissions are about equal.

The relative sizes of the mean and median amounts of carbon monoxide emissions cannot be inferred from the histogram.

In the data set shown below, the correlation coefficient of the two variables is:

**6.**

The data in the Excel spreadsheet linked below give the ages and salaries of the chief executive officers of 59 companies with sales between $5 million and $350 million.

The correlation between age and salary can be characterized as:

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·

Strong and positive.

·

Strong and negative.

·

Weak and positive.

·

Weak and negative

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-1.0.

-0.5

0.0

None of the above

43.

Electronics manufacturer SE must decide whether or not to invest in the development of a new type of battery. If the development succeeds, the market for the battery may be large or small. If it doesn’t succeed, the development efforts may or may not generate minor innovations that would offset some of the battery’s development costs. The tree below summarizes the decision.

The EMV of developing the new battery is $300,000. Based on EMV, SE should develop the battery. Given that development is successful, for what endpoint values for a large market does developing the battery have a lower EMV than not developing the battery?

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Less than $1.2 million.

Greater than $1.2 million.

Greater than $0.75 million.

None of the above.

44.

The manager of the Eris Shoe Company must decide whether or not to contract a controversial sports celebrity as its spokesperson. The new spokesperson’s value to Eris depends heavily on consumers’ perception of him. An initial decision analysis based on available data reveals that the expected monetary value of contracting the new spokesperson is $260,000. For $50,000 Eris can engage a market research firm that will help Eris learn more about how consumers might react to the celebrity. The EMV of buying this **sample information** (assuming it is free) for this decision is $300,000.

The tree below summarizes Eris’s decision. Based on EMV analysis, Eris’s manager should:

Hire the research firm.

Not hire the research firm, but contract the new spokesperson.

Not hire the research firm and not contract the new spokesperson.

The answer cannot be determined from the information

**7.**

7. For a given set of data, the standard deviation measures:

The difference between the mean and the data point farthest from the mean.

The difference between the mean and the data point nearest to the mean.

The difference between the mean and the median.

None of the above

**5.**

In the data set shown below, the correlation coefficient of the two variables is:

-1.0.

-0.5

0.0

None of the above

**8.**

The data in the Excel spreadsheet linked below give the average exchange rates of four currencies to the US dollar during October 2002.

Over this period, which currency was most volatile relative to the US dollar, as measured by the coefficient of variation?

The Brazilian Real.

The Euro.

The Japanese Yen.

The South Korean Won

**9.**

A national business magazine intends to survey its subscribers to determine who they think is the “CEO of the Century.” Subscribers are invited to complete an online survey.

Based only on this information, which of the following can be inferred about the survey results?

They will be biased because the magazine’s subscribers are unqualified to determine who the CEO of the century is.

They will accurately reflect the opinion of the nation as a whole about who the CEO of the century is.

They will be unbiased because the respondents will be self-selected.

They will be biased because subscribers who have access to the online survey are not representative of the population of subscribers as a whole.

10.

A political consultant conducts a survey to determine what position the mayoral candidate she works for should take on a proposed smoking ban in restaurants.

Which of the following survey questions will deliver an unbiased response?

Should the city ban smoking in restaurants to protect our children from second-hand smoke?

Should tobacco smoke, a known cause of lung cancer, be banned from public spaces such as restaurants?

Does the city have the right to restrict recreational activities, such as moderate consumption of alcohol or tobacco, on the premises of privately-owned businesses?

None of the above

11.

In a recently administered IQ test, the scores were distributed normally, with mean 100 and standard deviation 15.

What proportion of the test takers scored between 70 and 130?

About 68%.

About 84%.

About 95%.

About 99.5%.

12.

Which of the following is not true about the Normal Distribution?

It is symmetric.

Its mean and median are equal.

It is completely described by its mean and its standard deviation.

It is bimodal.

13.

The histogram below shows the underlying distribution pattern of the results of a rolled die. Suppose the die is rolled 50 times and the results are averaged. Suppose this process — rolling 50 dice and averaging their results — is repeated 100 times.

Which of the following best describes the distribution of these 100 averages?

Skewed right.

Skewed left.

Normal.

Uniform.

14.

A nutrition researcher wants to determine the mean fat content of hen’s eggs. She collects a sample of 40 eggs. She calculates a mean fat content of 23 grams, with a sample standard deviation of 8 grams. From these statistics she calculates a 90% confidence interval of [20.9 grams, 25.1 grams].

What can the researcher do to decrease the width of the confidence interval?

Increase the confidence level.

Decrease the confidence level.

Decrease the sample size

None of the above.

15.

In a random sample of 321 senior citizens, 61 were found to own a home computer.

Based on this sample, the 95% confidence interval for the proportion of computer-owners among senior citizens is:

[2.6%; 7.4%].

[13.4%; 24.6%].

[14.7%; 23.3%].

The answer cannot be determined from the information given

16.

Preliminary estimates suggest that about 58% of students at a state university favor implementing an honor code.

To obtain a 95% confidence interval for the proportion of all students at the university favoring the honor code, what is the minimum sample size needed if the **total**width of the confidence interval must be less than 5 percentage points (i.e., the confidence interval should extend at most 2.5 percentage points above and below the sample proportion)?

375.

264.

1,498.

The answer cannot be determined from the information given.

17.

In a survey of twelve Harbor Business School graduates, the mean starting salary was $93,000, with a standard deviation of $17,000.

The 95% confidence interval for the average starting salary among all Harbor graduates is:

[$83,382; $102,618].

[$82,727; $103,327].

[$82,199; $103,801].

[$59,000; $127,000].

18.

In a survey of 53 randomly selected patrons of a shopping mall, the mean amount of currency carried is $42, with a standard deviation of $78.

What is the 95% confidence interval for the mean amount of currency carried by mall patrons?

[$39.1; $44.9].

[$24.4; $59.6].

[$21.0; $63.0].

[$14.4; $69.6].

19.

A filling machine in a brewery is designed to fill bottles with 355 ml of hard cider. In practice, however, volumes vary slightly from bottle to bottle. In a sample of 49 bottles, the mean volume of cider is found to be 354 ml, with a standard deviation of 3.5 ml.

At a significance level of 0.01, which conclusion can the brewer draw?

The true mean volume of all bottles filled is 354 ml.

The machine is not filling bottles to an average volume of 355 ml.

There is not enough evidence to indicate that the machine is not filling bottles to an average volume of 355 ml.

The machine is filling bottles to an average volume of 355 ml.

20.

To conduct a one-sided hypothesis test of the claim that houses located on corner lots (corner-lot houses) have higher average selling prices than those located on non-corner lots, the following alternative hypothesis should be used:

The average selling price of a corner-lot house is higher than it is commonly believed to be.

The average selling price of a corner-lot house is higher than the average selling price of all houses.

The average selling price of a corner-lot house is the same as the average selling price of a house not located on a corner lot.

The average selling price of a corner-lot house is higher than the average selling price of a house not located on a corner lot.

21.

The data in the Excel spreadsheet linked below indicate the selling prices of houses located on corner lots (“corner-lot houses”) and of houses not located on corner lots.

Conduct a one-sided hypothesis test of the claim that corner-lot houses have higher average selling prices than those located on non-corner lots. Using a 99% confidence level, which of the following statements do the data support?

Upscale, expensive neighborhoods have more street corners.

The average selling price of a corner-lot house is higher than that of the average house not located on a corner lot.

The average selling price of a corner-lot house is no more than that of the average house not located on a corner lot.

There is not enough evidence to support the claim that the average selling price of a corner-lot house is higher than that of the average house not located on a corner lot.