# A market research firm wants to find out if men and women feel

21.
A market research firm wants to find out if men and women feel differently about SilkyTouch facial tissues. In a survey of 90 men, 76% said they had a favorable impression of SilkyTouch. Out of 182 surveyed women, 64% said they had a favorable impression of SilkyTouch.

At a 95% confidence level, which conclusion should the research firm draw?

Overall, about 70% of the population has a favorable impression of SilkyTouch.
Men and women feel differently about SilkyTouch.
More women than men have a favorable impression of SilkyTouch.
There is insufficient evidence to show that men and women feel differently about SilkyTouch

22.

A campaign strategist wants to determine whether demographic shifts have caused a drop in allegiance to the Uniformian Party in Bowie County. Historically, around 62% of the county’s registered voters have supported the Uniformians. In a survey of 196 registered voters, 57% indicated that they would vote for the Uniformians in the next election.

Assuming a confidence level of 95% and conducting a one-sided hypothesis test, which of the following should the strategist do?

Accept the hypothesis that the proportion of Uniformian voters has not changed.
Accept the hypothesis that the proportion of Uniformian voters has decreased.
Conclude that the proportion of Uniformian voters is now between 56% and 62%.
There is not enough evidence to support the hypothesis that the proportion of Uniformian voters has decreased.
23.

A manufacturer of guitar amplifiers markets one of its models, Vagabond, at a power rating of 45 watts. GuitarGod magazine suspects that this rating is inaccurate for this year’s model of the amp. In a random sample of 32 units of this year’s version of the Vagabond the mean output power is 42 watts, with a standard deviation of 8 watts.

Assuming a confidence level of 95%, which of the following statements do these data support?

This year’s Vagabond’s output power is 45 watts.
This year’s Vagabond’s output power is 42 watts.
This year’s Vagabond’s output power is not 45.
None of the above.

24.

The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable “average monthly temperature” (in degrees Fahrenheit).
At what level of significance is the relationship between ice cream consumption and temperature statistically significant?
Ice Cream Consumption and Temperature
Source

0.05
0.01
0.001
All of the above.

25.
The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable “average monthly temperature” (in degrees Fahrenheit).

Based on this analysis we can conclude:
Ice Cream Consumption and Temperature
Source

For every increase of 0.027 degrees in average monthly temperature, average ice cream consumption increases by 1 pint.

For every increase of 1 degree in average monthly temperature, average ice cream consumption increases by 0.027 pints.

For every increase of 1.797 degrees in average monthly temperature, average ice cream consumption increases by 1 pint.

For every increase of 1 degree in average monthly temperature, average ice cream consumption increases by 1.797 pints.

26.
The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable “average monthly temperature” (in degrees Fahrenheit).

Which of the following statements about the term “1.797” is true?

Ice Cream Consumption and Temperature
Source
It tells us the maximum amount above which ice cream consumption cannot possibly grow.
It tells us the minimum amount below which ice cream consumption cannot possibly fall.
It tells us the x-intercept of the regression equation.
It tells us the y-intercept of the regression equation.

27.
The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable “average monthly temperature” (in degrees Fahrenheit).

A reasonably accurate prediction would be that:

If the average monthly temperature is 48 degrees, average per household ice cream consumption will be around 3.1 pints.
If average monthly temperature is 48 degrees, average per household ice cream consumption will be around 2.6 pints.
If average monthly temperature is 48 degrees, average per household ice cream consumption will be around 86.3 pints.
If average monthly temperature is 48 degrees, average per household ice cream consumption will be around 1.3 pints.

28.
The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variable “average monthly temperature” (in degrees Fahrenheit). The Multiple R value, 0.8409 tells us the correlation between the dependent and independent variables. The R-squared value is 71%.

Based on these measures, we can conclude that:

The variation in average monthly temperature explains about 71% of the variation in household ice cream consumption.
The variation in average monthly temperature explains about 84% of the variation in household ice cream consumption.
Predictions about future household ice cream sales will be correct within a 71% confidence interval.
Predictions about future household ice cream sales will be correct within an 84% confidence interval.

29.
The scatter diagram and regression line below characterize the relationship between monthly ice cream consumption (in pints per household) and the independent variable “average monthly temperature” (in degrees Fahrenheit).

The residual errors are defined as:

The vertical distances from the data points to the horizontal axis.
The horizontal distances from the data points to the vertical axis.
The vertical distances from the data points to the regression line.
The shortest distance from the data points to the regression line.

30.
The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variables “average monthly temperature” (in degrees Fahrenheit) and “average price” (in dollars per pint).

At a significance level of 0.05, which independent variables contribute significantly to the consumption of ice cream?

Ice Cream Consumption, Temperature and Price
Source
Average monthly temperature only.
Average price of a pint of ice cream only.
Both independent variables.
Neither independent variable

31.
The regression analysis below characterizes the relationship between monthly ice cream consumption (in pints per household) and the independent variables “average monthly temperature” (in degrees Fahrenheit) and “average price” (in dollars per pint).

The coefficient of 0.027 for average monthly temperature informs us about:

Ice Cream Consumption, Temperature and Price
Source
The relationship between temperature and ice cream consumption when not controlling for price (i.e. allowing price to range freely).
The relationship between temperature and ice cream consumption when controlling for price (i.e. fixing price).
The relationship between temperature and ice cream price when controlling for consumption (i.e. fixing consumption).
The relationship between temperature and ice cream price when not controlling for consumption (i.e. allowing consumption to range freely).

32.
The regression analysis below characterizes the relationship between the current month’s ice cream consumption (in pints per household) and the independent variables “current month’s average temperature” (in degrees Fahrenheit), “previous month’s average temperature” (in degrees Fahrenheit), and “average price” (in dollars per pint).

In this analysis, the variable “previous month’s temperature” is:

Ice Cream Consumption, Two Months Temperatures
and Price
Source
A lagged variable.
A dependent variable.
Not statistically significant at the 0.05 level.
All of the above.

33.
The regression analysis at the bottom characterizes the relationship between the daily number of visitors at an amusement park and the variable “school day.” “School day” is an independent variable that is equal to 1 when a given day is a school day and equal to 0 when it is not.

The coefficient of -13,644 tells us that:

Amusement Park Visitors
Source
On average, the number of visitors on school days is 13,644 lower than on non-school days.
On every school day, the number of visitors is exactly 13,644 lower than on non-school days.
On average, the number of visitors on school days is 13,644.
On average, the number of visitors on non-school days is 13,644.

34.
When an additional independent variable is added to a regression analysis, which of the following could be indications of multicollinear independent variables?

Source
A drop in R-squared and a drop in significance for one or more independent variable.
A drop in adjusted R-squared and an increase in significance for one or more independent variable.
An increase in adjusted R-squared and an increase in significance for one or more independent variable.
An increase in adjusted R-squared and a drop in significance for one or more independent variable.

35.
In a regression analysis, which of the following cannot happen when a new independent variable is added?

Source
R-squared increases and adjusted R-squared increases.
R-squared increases and adjusted R-squared decreases.
R-squared decreases and adjusted R-squared decreases.
Any of the above can occur when a new independent variable is added

36.
The table below displays data on the composition and performance of the Massachusetts Bubble Growth (MBG) technology stock fund over the last year. The table includes data on the distribution of stocks in the fund by technology sector (information technology (IT) or biotechnology) and by last year’s “performance” (positive or negative net change in share price over the last year).

What is the probability that a randomly-chosen MBG stock is a biotech stock?

Source
30%
23%
7%
None of the above.

37.
The table below displays data on the composition and performance of the Massachusetts Bubble Growth (MBG) technology stock fund over the last year. The table includes data on the distribution of stocks in the fund by technology sector (information technology (IT) or biotechnology) and by last year’s “performance” (positive or negative net change in share price over the last year).

What is the conditional probability that an MBG stock had a positive change in share price, given that it is an IT stock?

24.3%
42.5%
40.0%
None of the above

38.
The table below displays data on the composition and performance of the Massachusetts Bubble Growth (MBG) technology stock fund over the last year. The table includes data on the distribution of stocks in the fund by technology sector (information technology (IT) or biotechnology) and by last year’s “performance” (positive or negative net change in share price over the last year).

Regarding the stocks that made up the MBG fund last year, which of the following statements is true?

Technology sector and performance are statistically independent.
The fact that a given stock’s performance was positive tells us nothing about its sector.
The fact that a given stock is from the biotech sector tells us nothing about its performance.
None of the above

39.
Jaune Magazine (JM) must decide whether or not to publish a tell-all story about a celebrity. If the story ends up having major impact, JM will realize substantial profits from additional magazine sales, subscriptions, and advertising revenues. However, if JM publishes the story, JM will face a lawsuit; if it loses the suit, the penalties could be substantial. The tree below summarizes JM’s decision.

What is the expected monetary value of publishing the story?
\$10,000
-\$10,000
\$26,000
\$90,000

40.
Jaune Magazine (JM) must decide whether or not to publish a tell-all story about a celebrity. If the story ends up having major impact, JM will realize substantial profits from additional magazine sales, subscriptions, and advertising revenues. However, if JM publishes the story, JM will face a lawsuit; if it loses the suit, the penalties could be substantial. The tree below summarizes JM’s decision.

The EMV of publishing the story is \$10,000. Based on this EMV, JM should publish the story. If the publisher chooses not to publish the story, which of the following best describes the publisher’s attitude towards this decision?

Risk averse.
Risk neutral
Risk seeking.
Risqué.

41.
Jaune Magazine (JM) must decide whether or not to publish a tell-all story about a celebrity. If the story ends up having major impact, JM will realize substantial profits from additional magazine sales, subscriptions, and advertising revenues. However, if JM publishes the story, JM will face a lawsuit; if it loses the suit, the penalties could be substantial. The tree below summarizes JM’s decision.

The EMV of publishing the story is \$10,000. Based on this EMV, JM should publish the story. For what values of p = Prob[story has major impact] is publishing the story preferable to not publishing the story on the basis of EMV?

Source

p [removed] 10%

p < 90%

None of the above.

42.
Jaune Magazine (JM) must decide whether or not to publish a tell-all story about a celebrity. If the story ends up having major impact, JM will realize substantial profits from additional magazine sales, subscriptions, and advertising revenues. However, if JM publishes the story, JM will face a lawsuit; if it loses the suit, the penalties could be substantial. The tree below summarizes JM’s decision.

If JM publishes the story, the publisher may feel remorse for having violated the celebrity’s privacy. For what values of the cost of remorse would not publishing the story be preferable to publishing the story on the basis of EMV?

Source
Higher than \$10,000
Lower than \$10,000
Lower than \$12,500
None of the above.

43.
The manager of the Regal Beverage Company (RBC) must decide whether or not to market a new soft drink flavor. The new drink’s success depends heavily on consumer reaction to it. An initial decision analysis based on available data reveals that the expected monetary value of marketing the new drink is -\$200,000. The EMV of buying perfect information for this decision is \$50,000, as shown in the tree below. A market research firm offers to do market research for RBC at a cost of \$30,000. Although not perfect, the market research should give RBC some information about potential customer reaction to the new flavor.
Based on an EMV analysis, RBC’s manager should:

Source
Buy the research firm’s sample information.
Not buy the research firm’s sample information, but market the new drink.
Not buy the research firm’s sample information and not market the new drink.
The answer cannot be determined from the information provided.

(550 words)

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