# Harvard Quantitative Methods Final Assessment Test 2

Q1. 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. Which of the following statements is true?

- The fact that a CD has a content error tells us nothing about whether it has a labeling error.
- The events of a CD having a content error and a CD having a labeling error are statistically dependent.
- The fact that a CD has a labeling error tells us something about whether it has a content error.
- None of the above.

Q2. 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

Q3. 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, what is the expected energy consumption?

- Around 90,711 trillion BTUs
- Around 91,501 trillion BTUs
- Around 28,016 trillion BTUs
- Around 467,729 trillion BTUs

Q4. The WH meat-packing company must decide whether or not to recall one week’s production of kielbasa due to possible contamination. An outbreak of non-fatal food poisoning may be linked to WH. If so, WH may face a lawsuit. The tree below summarizes the decision. The EMV of the cost of **not** issuing a recall is $80,000. Based on EMV, the manager should not issue the recall. For what values of **p** = Prob[WH is implicated] is not recalling the kielbasa preferable to recalling the kielbasa, in terms of EMV?

- p < 15%
- p > 15%
- p < 85%
- None of the above

Q5. The data in the Excel spreadsheet linked below gives the average monthly price of gold (in dollars per ounce) for the years 1980 to 1983. In which of the years was the coefficient of variation of gold price the highest?

- 1981
- 1982
- 1983
- 1980

Q6. 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

Q7. 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

Q8. In a regression analysis with multiple independent variables, what causes multicollinearity?

- A strong linear relationship between two or more independent variables
- A strong nonlinear relationship between the dependent variable and one or more independent variables
- A strong heteroskedastic relationship between the dependent variable and one or more independent variables
- None of the above

Q9. 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.

Q10. A researcher wants to collect data about the study habits of sophomores at Harmond University. From the sophomore class of 2,300 students, she wants to collect a sample of 70 students. Which of the following sampling methods will yield the most representative sample?

- Assigning each sophomore a number and then randomly generating 70 numbers from that list
- Randomly selecting 70 sophomores entering the university’s main library on a randomly selected evening
- Selecting the 70 sophomores whose grade point averages (GPA) fall closest to the mean GPA of the sophomore class
- Randomly selecting 70 sophomores who are members of college fraternities

Q11. 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 conditional probability that a CD has no content errors, given that has a labeling error?

- 97.02%
- 1.98%
- 98.00%
- None of the above

Q12. The WH meat-packing company must decide whether or not to recall one week’s production of kielbasa due to possible contamination. An outbreak of non-fatal food poisoning may be linked to WH. If so, WH may face a lawsuit. The tree below summarizes the decision. What is the expected monetary value of the cost of **not** issuing a recall?

- $80,000
- $120,000
- $800,000
- $0

Q13. 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.

Q14. A telemarketing company wants to find out if people are more likely to answer the phone between 8 p.m. and 9 p.m. than between 7 p.m. and 8 p.m. Out of 96 calls between 7 p.m. and 8 p.m., 72 were answered. Out of 105 calls between 8 p.m. and 9 p.m., 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 8 p.m. and 9 p.m. is greater than the proportion who answer the phone between 7 p.m. and 8 p.m.
- People are more likely to answer the phone between 8 p.m. and 9 p.m.
- Telemarketers should not call at all during the evenings.
- People are more likely to answer the phone between 7 p.m. and 8 p.m

Q15. 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%

Q16. The data in the Excel spreadsheet linked below gives the average monthly price of gold (in dollars per ounce) for the years 1980 to 1983. 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

Q17. A company’s average accounts receivable per customer is $132.54. After a problem in the automated accounting software is suspected, a random sample of 38 accounts reveals a sample mean of $143.55 and a sample standard deviation of $38.29. After running a two-sided hypothesis test of the hypothesis that the average accounts receivable has changed, what is the best conclusion (using a 95% confidence level)?

- There is not sufficient evidence that the average accounts receivable has changed.
- The average accounts receivable is still $132.54.
- The average accounts receivable is at least $143.55.

Q18. The table below displays a week’s worth of data on daily sales at the Crank It Louder Music Store. Over that time period, what was the median daily level of sales?

- $1,643.23
- $3,489.79
- $3,130.46
- $800.12

Q19. 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, what should she do?

- 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.

Q20. What completely determines a normal distribution?

- Its mean and its standard deviation
- Its mean and its mode
- Its mean and its median
- None of the above

Q21. 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 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.

Q22. Which of the following correctly ranks from smallest to largest the measures of central tendency of the data displayed in the histogram below?

- Mode < mean < median
- Median < mode < mean
- Mode < median < mean
- Not enough information to determine the answer

Q23. The WH meat-packing company must decide whether or not to recall one week’s production of kielbasa due to possible contamination. An outbreak of non-fatal food poisoning may be linked to WH. If so, WH may face a lawsuit. The tree below summarizes the decision. The EMV of the cost of **not** issuing a recall is $80,000. Based on EMV, WH should not issue a recall. If WH chooses to recall, which of the following best describes the WH’s attitude towards this decision?

- Risk averse
- Risk neutral
- Risk seeking
- Chicken

Q24. The table below displays a week’s worth of data on daily sales at the Crank It Louder Music Store. Over that time period, what was the mean daily level of sales?

- $3,489.79
- $4,071.42
- $1,643.23
- $2,829.92

Q25. In a public opinion poll, 48% of 189 respondents favored an elimination of taxes on dividend income. What is the 95% confidence interval for the proportion of people who favor an elimination of taxes on dividend income?

- [40.9%, 55.1%]
- [47.5%, 48.5%]
- Not enough information to determine the answer

Q26. 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.

Q27. The WH meat-packing company must decide whether or not to recall one week’s production of kielbasa due to possible contamination. An outbreak of non-fatal food poisoning may be linked to WH. If so, WH may face a lawsuit. The tree below summarizes the decision. The EMV of the cost of **not** issuing a recall is $80,000. Based on EMV, WH should not issue a recall. An estimated value of a reputation loss is included in the outcome estimate of the lawsuit. If WH is implicated, the firm may face a reputation loss even if no lawsuit is filed. For what values of that reputation loss would issuing the recall be preferable, in terms of EMV?

- Higher than $500,000
- Lower than $500,000
- Lower than $44,444
- None of the above

Q28. The histogram below displays the age distribution of the world’s billionaires as reported by Forbes Magazine in 2001. What is the best way to describe this distribution?

- Approximately normal
- Strongly skewed to the right
- Bimodal
- Approximately uniform

Q29. In a finance course at a business school, 6 students are randomly selected. Their mean score on the final exam is 75, with standard deviation 8. What is the 95% confidence interval for the average class score on the final?

- [66.6, 83.4]
- [67.6, 82.4]
- [71.7, 78.3]

Q30. 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

Q31. 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.” 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.

Q32. 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
- None of the above

Q33. In a public opinion poll, 48% of 189 respondents favor an elimination of taxes on dividend income. How many respondents would be needed to calculate a 95% confidence interval (for the proportion of people who favor an elimination of taxes on dividend income) that has a total width no greater than 4% (i.e., the estimate must be within +/- 2% of the true population proportion)?

- 2,398
- 600
- 1,689
- Not enough information to determine the answer

Q34. The scatter diagram below displays the relationship between age and net worth (in US$ billions) for the world’s 20 wealthiest people as reported by Forbes Magazine in 2001. If 45-year-old Bill Gates, the world’s wealthiest person, is considered an outlier and removed from the data set, what will be the effect on this relationship?

- The value of the correlation coefficient will decrease.
- The value of the correlation coefficient will stay about the same.
- The correlation will become perfectly linear.

Q35. The data in the Excel spreadsheet linked below gives the net worth (in US$ billions) and ages of the world’s billionaires as reported by Forbes Magazine in 2001. What is the correlation coefficient between age and net worth?

- About 0.00
- Greater than 0.5
- Less than -0.5
- Not enough information to determine the answer

Q36. 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.

Q37. A company’s average accounts receivable per customer is $132.54. After a problem in the automated accounting software is suspected, a random sample of 38 accounts reveals a sample mean of $143.55 and a sample standard deviation of $38.29. In a two-sided hypothesis test to see if the average accounts receivable has changed, what is the best formulation of the null hypothesis?

- The average accounts receivable is $132.54.
- The average accounts receivable is $143.55.
- The average accounts receivable is no longer $132.54.
- None of the above.

Q38. 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.

Q39. The WH meat-packing company must decide whether or not to recall one week’s production of kielbasa due to possible contamination. An outbreak of non-fatal food poisoning may be linked to WH. If so, WH may face a lawsuit. The tree below summarizes the decision. The EMV of the cost of **not** issuing a recall is $80,000. Suppose there were a way to know for certain whether WH would be implicated or not. What would be the value of this perfect information?

- $68,000
- $12,000
- $80,000
- None of the above

Q40. A manufacturer of microwaves gathers information on microwave sales from a random sample of 50 stores in a large retail chain. In the sample, the mean number of microwaves sold per store last week was 19, with standard deviation 2. What is the 95% confidence interval for the mean number of microwaves sold at a retail store in the chain last week?

- [18.45, 19.55]
- [17.00, 21.00]
- [15.00, 23.00]
- [18.27, 19.73]

Q41. The regression analysis below relates US annual energy consumption in trillions of BTUs to the independent variables “US Gross Domestic Product (GDP) in trillions of dollars” and “average gas mileage of all passenger cars in miles per gallon (mpg).” The coefficient for the independent variable “average car gas mileage (mpg),” -70.50, describes

- the relationship between energy consumption and average car gas mileage, controlling for GDP.
- the relationship between energy consumption and average car gas mileage, not controlling for GDP.
- the relationship between average car gas mileage and GDP, controlling for energy consumption.
- the relationship between average car gas mileage and GDP, not controlling for energy consumption.

Q42. The regression analysis below relates US annual energy consumption in trillions of BTUs to the independent variables “US Gross Domestic Product (GDP) in trillions of dollars” and “average gas mileage of all passenger cars in miles per gallon (mpg).” Which of the two independent variables is significant at the 0.01 level?

- GDP only
- Average car gas mileage only
- Both independent variables
- Neither independent variable

Q43. When calculating a confidence interval for a mean, which of the following will increase the width of the confidence interval?

- Decreasing the sample size
- Increasing the sample size
- Increasing the sample mean

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