# STATS 456 Unit Questions 2015

October 22, 2018

Use the problem below to answer the questions that follow.
Before the presidential debates, it was expected that the
percentages of registered voters in favor of various candidates to be as
follows.

Percentages

Democrats

48%

Republicans

38%

Independent

4%

Undecided

10%

After
the presidential debates, a random sample of 1200 voters showed that 540
favored the Democratic candidate; 480 were in favor of the Republican
candidate; 40 were in favor of the Independent candidate, and 140 were undecided.
At a 1% level of significance, test to see if the proportion of voters has
changed.

Question 1
1. What is the best type
of hypothesis test to apply for this problem?

Analysis of Variance (ANOVA)

Chi Square Goodness of Fit Test

Chi-Square Test of Independence

Question 2
1. State the hypothesis
test for this problem.

Ho: The proprtions of voters of each type are the
same after the presidential debates as they were before.
Ha: [At least 2 of] The proportions of voters of each
type are statistically significantly different before and after the
presidential debates.

Ho: [At least 2 of] The proportions of voters of each
type are statistically significantly different before and after the
presidential debates.
Ha: The proprtions of voters of each type are the
same after the presidential debates as they were before.

Ho: The proportions of voters are independet of party
affiliation.
Ha: There is a relationship between proportions
of voters and party affiliation.

Ho: There is a relationship between proportions of
voters and party affiliation.
Ha: The proportions of voters are independet of party
affiliation.

Question 3
1. For this problem, the
alpha level (the chance that you will incorrectly reject the null and draw an
incorrect conclusion) is:

0.48

1.00

0.01

0.04

3

Question 4
1. Calculate the value
of the Chi-Square Test Statistic for this problem. What is it?

Question 5
1. Identify the critical
value for this problem using the Table of Critical Values of the
Chi Square Distribution in your text. What is the critical value?

Question 6
1. What is your
conclusion for this problem?

Statistically, the proportions of voters of each type remained
the same before and after the debates.

There are statistically significant differences in the
proportions of each type of voter before and after the presidential debates..

There is a relationship between the proportions and presidential
debates.

The presidential debates are independent of party affiliation..

Proportions in income level and gender do not statistically
significantly change over time.

­__________________________________________________________________

Questions 1 – 6 of this quiz refer to the problem below.
.A sample of 150 individuals (males and females) was
surveyed, and the individuals were asked to indicate their yearly incomes.
The results of the survey are shown below.

Income
Category

Male

Female

Category 1: \$20,000 up to \$40,000

10

30

Category 2: \$40,000 up
to \$60,000

35

15

Category 3: \$60,000 up
to \$80,000

15

45

Test
at?= 0.05 to determine if
the yearly income is independent of the gender.

.gif” alt=”Expand”>What is the best type of hypothesis
test to apply for this problem?

Analysis of Variance (ANOVA)

Chi Square Goodness of Fit Test

Chi-Square Test of Independence

Question 2
1. State the
hypothesis test for this problem.

Ho: Income level and gender proportions are the
same in this sample as in a larger population.
Ha: income level and gender proportions are
different in this sample than in the larger population.

Ho: Income level and gender are
independent.
Ha: There is a relationship between income
level and gender.

Ho: There is a relationship between income level
and gender.
Ha: Income level and gender are
independent.

Ho: Income level and gender are independent.
Ha: Income level depends on gender.

Question 3
1. In this problem,
the level of significance is:

150 total people in the sample.

\$80,000, the maximum income value.

60 and 90, the total number of men and women in the sample,
respectively.

0.05, the highest probability/chance that you are willing to risk
of incorrectly rejecting the null hypothesis.

(# of rows – 1)(# of columns – 1) = (2 – 1)(3 –
1) = (1)(2) = 2 degrees of freedom (df)

Question 4
1. Calculate the value
of the Chi-Square Test Statistic for this problem. What is it?

Question 5
1. Identify the
critical value for this problem using the Table of Critical Values of
the Chi Square Distribution. What is the critical value?

Question 6
1. What is your
conclusion for this problem?

Gender depends on income level.

Income level depends on gender.

There is a relationship between income level and gender.

Income level and gender are independent.

Proportions in income level and gender do not statistically
significantly change over time
_______________________________________________________

Questions 1 – 10 refer to
the problem that follows.

Investors in mutual
funds keep a sharp eye on the total return on their money. They also are
aware of the risk
involved in their investment, commonly measured by a fund’s volatility (the
greater the
volatility, the higher the risk). Below is a list of 30 mutual funds randomly
selected in
1998 from Fortune’s
list of stock and bond funds, together with their 5-year total return (%)
and
risk assessment:

Fund Name Total Return
Risk

MFS Emerging Growth

21.5

20.6

Kaufmann

19.7
18.4

AIM Constellation A

17.6
18.4

Weitz Hickory

29.9
19.7

Oak Value

25.6

13.0

Gabelli Westwood
Equity

23.0

12.3

Nationwide

24.3

12.0

Fidelity
Growth/Income

22.6

13.0

Stratton Growth

21.3
11.8

GAM International A

22.6
19.9

Scudder
International

14.3

13.7

.
Janus
Worldwide 23.6

13.7

Oppenheimer Global A

19.0

14.4

New
Perspective 18.8

12.1

Putnam Europe Growth
A 22.7

14.6

AIM Balanced A
1

5.9

10.8
Delaware A

13.6

8.6
Greenspring

14.0

7.2
Calamos Convertible
A

14.3

9.9
Managers Bond

10.3
5.4
Harbor Bond

7.3

4.4
Northeast Investors

3.6

5.5
Strong Gov’t.
Securities

7.0

4.4
Lexington GNMA
Income 6.9

3.5
Marshall Gov’t.
Income

5.8

3.7
Wright U.S. Treasury

6.3

7.5
Excelsior Tax-Exempt

7.6

6.7
Vanguard Municipal

6.5

5.5
Goldman Sachs Global

7.2

4.1
Capital World Bond

5.9
4.9

Source: Fortune,
“The Best Mutual Funds”, August 17, 1998, pp. 88-98.

Suppose that the question
you wish to address using this data is whether the total return on the
investment is affected by the risk of the investment. You also want to know
if you can predict the total return based on the risk. You will attempt a
these questions.

Question 1
1. Which
variable in this problem would be considered the independent variable?

Company

Total Revenue

Risk

Time

Question 2
1. Which
variable in this problem would be considered the dependent variable?

Company

Total Revenue

Risk

Time

Question 3
1. Sketch a
scatter plot (scatter diagram) of the data above. The graph indicates that the
relationship between Total Return and Risk is

positive-as risk
increases, total return increases.

negative- as risk increases, total return decreases.

zero- as risk increases, total return remains relatively
constant.

does not exist—total risk remains relatively constant.

Question 4
1. Use Micrsoft Excel 2010 to run a linear regression analysis. What
is the value of R2 (R-squared)?

Question 5
1. What does this value for R2 (R-squared) suggest about
the linear equation that Excel determines as the line of best fit?

This equation will be a
very good predictor of related data values.

This equation will be an
acceptable predictor of related data values.

This equation will be a poor predictor of related data values.

Inconclusive value

Question 6
1. Identify the coefficients from the Excel Output summary that are
used to write the line of best fit for this data. If the equation
was written as

y = b1x
+ b0,

where y
if the total return value and x is the risk, what is the
value of b0?

Question 7
1.
Identify the coefficients from the
Excel Output summary that are used to write the line of best fit for this
data. If the equation was written as

y = b1x + b0,

where y if the total return value and x is the risk, what is
the value of b1?

Question 8
1. What does the value of b0 represent?

the amount total revenue
will change when the risk is increased by 1

the value of the total
revenue if the risk was 0

the value of the risk if
the total revenue was 0

the amount that risk will
increase if total revenue increases by 1

Question 9
1. What does
the value of b1 represent?

the amount total revenue
will change when the risk is increased by 1

the value of the total
revenue if the risk was 0

the value of the risk if
the total revenue was 0

the amount that risk will
increase if total revenue increases by 1

Question 10
1.
Use the line of best fit to
predict the total return (y-value) for a risk of x = 11?

Total Return = _________ ?

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