# Mathematics

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?

Source

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:

Source

[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 totalwidth 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)?

Source

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:

Source

[\$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?

Source

[\$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?

Source

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:

House Prices Data
Source

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?

House Prices Data
Source

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.

22.

Two semiconductor factories are being compared to see if there is a difference in the average defect rates of the chips they produce. In the first factory, 250 chips are sampled. In the second factory, 350 chips are sampled. The proportions of defective chips are 4.0% and 6.0%, respectively.

Using a confidence level of 95%, which of the following statements is supported by the data?

Source

There is not sufficient evidence to show a significant difference in the average defect rates of the two factories.

There is a significant difference in the average defect rates of the two factories.

The first factory’s average defect rate is lower than the second factory’s on 95 out of 100 days of operation.

None of the above.

23.

The regression analysis below relates average annual per capita beef consumption (in pounds) and the independent variable “average annual beef price” (in dollars per pound).

The coefficient on beef price tells us that:

Beef Consumption and Price
Source

For every price increase of \$1, average beef consumption decreases by 9.31 pounds.

For every price increase of \$1, average beef consumption increases by 9.31 pounds.

For every price increase \$9.31, average beef consumption decreases by 1 pound.

For price increase of \$9.31, average beef consumption increases by 1 pound

24.

The regression analysis below relates average annual per capita beef consumption (in pounds) and the independent variable “average annual beef price” (in dollars per pound).

In a year in which the average price of beef is at \$3.51 per pound, we can expect average annual per capita beef consumption to be approximately:

Beef Consumption and Price
Source

55.2 pounds

52.6 pounds

53.6 pounds

117.9 pounds

25.

The regression analysis below relates average annual per capita beef consumption (in pounds) and the independent variable “average annual per capita pork consumption” (in pounds).

At what level is the coefficient of the independent variable pork consumption significant?

Beef Consumption and Pork Consumption
Source

0.10.

0.05.

0.01.

None of the above

26.

The regression analysis below relates average annual per capita beef consumption (in pounds) and the independent variable “average annual per capita pork consumption” (in pounds).

Which of the following statements is true?

Beef Consumption and Pork Consumption
Source

Beef consumption can never be less than 65.09 pounds.

Beef consumption can never be greater than 65.09 pounds.

The y-intercept of the regression line is 65.09 pounds.

The x-intercept of the regression line is 65.09 pounds.

27.

The regression analysis at the bottom relates average annual per capita beef consumption (in pounds) and the independent variables “average annual per capita pork consumption” (in pounds) and “average annual beef price” (in dollars per pound).

Which of the independent variables is significant at the 0.01 level?

Beef Consumption, Pork Consumption, and Beef Price
Source

Beef price only.

Pork consumption only.

Both independent variables.

Neither independent variable.

28.

The regression analysis at the bottom relates average annual per capita beef consumption (in pounds) and the independent variables “annual per capita pork consumption” (in pounds) and “average annual beef price” (in dollars per pound).

The coefficient for beef price, -12, tells us that:

Beef Consumption, Pork Consumption, and Beef Price
Source

For every \$1 increase in beef price, average beef consumption decreases by 12 lbs, not controlling for pork consumption.

For every \$12 drop in beef price, average beef consumption decreases by 1 lbs, not controlling for pork consumption.

For every \$1 increase in beef price, average beef consumption decreases by 12 lbs, controlling for pork consumption, i.e. holding pork consumption constant.

For every \$12 decrease in beef price, average beef consumption decreases by 1 lbs, controlling for pork consumption, i.e. holding pork consumption constant.

29.

The data in the Excel spreadsheet linked below give the seasonally adjusted value of total new car sales (in millions of dollars) in the United States, total national wage and salary disbursements (referred to here as “compensation”) (in billions of dollars), and the employment level in the non-agricultural sector (in thousands) for 44 consecutive quarters. An auto industry executive wants to know how well she can predict new car sales two quarters in advance using the current quarter’s compensation data.

How many data points can she use in a regression analysis using the data provided?

Car Sales Data
Source

41.

42.

43.

44.

30.

The Excel spreadsheet linked below contains the simple regressions of total new car sales (in millions of dollars) on each of two independent variables: “compensation” (in billions of dollars) and “employment level in the non-agricultural sector” (in thousands) .

Which of the following independent variables explains more than 90 percent of the observed variation in new car sales?

Car Sales Simple Regressions
Source

Compensation only.

Employment level only.

Both independent variables

31.

The regression analysis below relates the value of new car sales (in millions of dollars) to compensation (in billions of dollars) and the employment level in the non-agricultural sector (in thousands) for 44 consecutive quarters.

Which of the two independent variables is statistically significant at the 0.05 level?

Car Sales Multiple Regression
Source

Compensation only.

Employment level only.

Both independent variables.

Neither independent variable.

32.

The regression analysis below relates the value of new car sales (in millions of dollars) and the independent variables “compensation” (in billions of dollars) and “employment level in the non-agricultural sector” (in thousands) for 44 consecutive quarters. Compare this multiple regression to the simple regressions with compensation and employment level as the respective independent variables.

Which of the following is the likely culprit of the dramatic increase in the p-value for employment level in the multiple regression?

Car Sales Regressions
Source

Multicollinearity.

Heteroskedasticity.

Nonlinearity.

None of the above

33.

The regression analysis below relates the value of new car sales (in millions of dollars) and the independent variables “compensation” (in billions of dollars) and “employment level in the non-agricultural sector” (in thousands) for 44 consecutive quarters.

The coefficient for employment level, 0.21, describes:

Car Sales Multiple Regression
Source

The behavior of car sales as the employments level changes, controlling for compensation.

The behavior of the employment level as car sales change, not controlling for compensation.

The behavior of car sales as the employment level changes, not controlling for compensation.

The behavior of the employment level as car sales change, controlling for compensation.

34.

A new blood pressure treatment is being tested. The regression analysis below describes the relationship between the 41 test subjects’ diastolic blood pressure and the dummy variable “medication.” When a test subject is taking the new drug, the value of medication is 1, when not, the value of medication is 0.

Which of the following can be inferred from the regression analysis?

Blood Pressure
Source

The medication has no statistically significant effect (at a 0.01 significance level).

The use of medication accounts for around 42% of the variation in diastolic blood pressure.

On average, test subjects taking the medication report a diastolic blood pressure level about 5 points lower than those not taking the medication.

None of the above.

35.

In a regression analysis, a residual plot is:

Source

A scatter diagram that plots the values of the residuals against the values of the dependent variable.

A scatter diagram that plots the values of the residuals against the values of an independent variable.

A histogram that plots the frequency of certain value ranges of the residuals.

None of the above.

36.

In a regression analysis, if a new independent variable is added and R-squared increases and adjusted R-squared decreases precipitously, what can be concluded?

Source

The new independent variable improves the predictive power of the regression model.

The new independent variable does not improve the predictive power of the regression model.

The regression was performed incorrectly. It is impossible for R-squared to increase and adjusted R-squared decrease simultaneously.

The new independent variable’s coefficient is not significant at the 0.01 level

37.

The table below displays data the First Bank of Silverhaven (FBS) has collected on the personal savings accounts of its job-holding customers. The table includes data on the distribution of the number of accounts held by Homeowners vs. Non-Homeowners, and by whether the customer is Self-Employed or is Employed by a firm in which he or she does not have an ownership stake.

What is the probability that a given account-holder is self-employed?

Source

15%

12%

3%

None of the above.

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