# STATS 456 Unit Questions 2015

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?

Hypothesis Test About The Means

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?

Hypothesis Test About The Means

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

Linear Regression Analysis Using Microsoft Excel 2010 to help you answer

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 = _________ ?

**30%**with the discount code: ESSAYHELP