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: 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: 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: For this problem, the alpha level (the chance that you will incorrectly reject the null and draw an incorrect conclusion) is:
QUESTION 4: Calculate the value of the Chi-Square Test Statistic for this problem. What is it?
QUESTION 5: 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: 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.
Refer to the problem below.
1) 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 α = 0.05 to determine if the yearly income is independent of the gender.
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
2) 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.
3) 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)
4) Calculate the value of the Chi-Square Test Statistic for this problem. What is it?
5) Identify the critical value for this problem using the Table of Critical Values of the Chi Square Distribution. What is the critical value?
6) 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 below 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.
1) Which variable in this problem would be considered the independent variable?
- Company
- Total Revenue
- Risk
- Time
2) Which variable in this problem would be considered the dependent variable?
- Company
- Total Revenue
- Risk
- Time
3) 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.
4) Use Micrsoft Excel 2010 to run a linear regression analysis. What is the value of R2 (R-squared)?
5) 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
6) 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?
7) 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?
8) 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
9) 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
10) Use the line of best fit to predict the total return (y-value) for a risk of x = 11?
Total Return = _________ ?