Week One: One Sample Hypothesis Testing



Week One: One Sample Hypothesis Testing

Objective: Identify the formal hypothesis testing process.

 1. If a null hypothesis is not rejected at the 0.10 level, it may be rejected at the 0.05 level. 

1. True

2. False 

Explanation: The null hypothesis is not rejected at the 0.10 level means the p – value is greater than 0.10. So, it is greater than 0.05 also.

Objective: Perform a hypothesis test of one proportion. 

2. The Roman Senate has become concerned about the loyalty of the army in Gaul commanded by Julius Caesar. They claim that of the 80,000 men in the army, at least 28,000 are foreign barbarians. Caesar believes that there are fewer barbarians than that, so the Senate should not worry. He polls one legion of 1,000 men and finds that 340 of them are barbarians.

Assume the value of the test statistic is -0.70. Calculate the p-value for this test using Excel. 

1. =NORMSDIST(-0.7)

2. =TDIST(-0.70,999,1)

3. =2*(NORMSDIST(-0.7))

4. =TDIST(0.7,999,2)

Explanation: We are conducting one tail Z test

 Objective: Perform a hypothesis test of one population mean using the standard normal distribution.

3. A pooled proportion estimate can be used to calculate the test statistic for a test of the equality of proportions when the

• a. populations are normally distributed

• b. sample sizes are small

• c. samples are independently drawn from the populations

• d. null hypothesis states that the two population proportions are equal

 Objective: Interpret the results of hypothesis tests.

 4. Sample sizes of two independent samples must be identical if we plan to test for a difference of means.

1. True

2. False

 Week Two: Two or More Sample Hypothesis Testing

Objective: Apply hypothesis testing to different populations and samples in business research situations.

 5. One characteristic of any Student's t distribution is

• a. It is right skewed.

• b. As n increases, the t-distribution approaches a uniform distribution.

• c. It is described by its degrees of freedom.

• d. It has a mean of 0 and a standard deviation of 1.

 Objective: Perform a hypothesis test of two population means using the standard normal distribution.

 6. One hundred women were polled and 60 reported successfully communicating an automobile problem to the auto repairman. A sample of 150 men had 95 reporting the same success. The value of the test statistic for a test of the equality of proportions is

1. -0.5319

2. 0.7293

3. -0.419

4. 0.2702

 Objective: Perform a hypothesis test of two proportions.

 7. There are no test questions associated with this objective.

 Objective: Determine when to use an ANOVA for managerial decisions.

 8. A balanced experiment requires that the sample size for each treatment be equal.

1. True

2. False

 Objective: Perform an ANOVA.

 9. If you have 4 factors (call them A, B, C and D) in an ANOVA experiment with replication you could have 4 different two-factor interactions.

1. True

2. False

 Week Three: Tests in Research Objective: Determine when to use nonparametric tests in business. 

10. There are no test questions associated with this objective.

 Objective: Differentiate among various nonparametric tests.

 11. My friend Linda is a real estate broker. She studied compared the asking price of homes in two different communities to their corresponding selling prices. The purpose was to compare the distribution of price ratios, asking to selling, in the two communities. Samples were selected from each community using last years information. What would be her best nonparametric method to analyze the data?

1. Friedman test

2. Spearman's rho

3. Kruskal-Wallis test

4. Wilcoxon signed-rank sum test

  Objective: Analyze data with chi-square.

 12. A recent study of four hundred accidents that occurred on a Saturday night were analyzed. Information collected was the number of vehicles involved and if alcohol played a role in the accident.

|Role of |Number of Vehicles Involved |

|Alcohol? | |

|  |1 |2 |3 |Totals |

|Yes |50 |100 |20 |170 |

|No |25 |175 |30 |230 |

|Totals |75 |275 |50 |400 |

Degrees of freedom for this test are:

• a. 4

• b. 3

• c. 2

• d. 1

Objective: Interpret the results of a nonparametric hypothesis test.

 13. Non-parametric tests that require a minimum of ordinal level data can be applied to interval or ratio data.

1. True

2. False

I am not sure

 Week Four: Regression Analysis in Research

Objective: Interpret the correlation coefficient.

 14. The quick rule would say that in a bivariate scatter plot with 25 observations, a correlation of 0.45 is significantly different than zero (but just barely).

1. True [pic]

• b. False

 Objective: Perform a linear regression.

15. One of the consequences of multicollinearity in multiple regression is biased estimates of the slope coefficients.

1. True

2. False

 Objective: Interpret the results of a simple regression.

16. The coefficient of determination is the coefficient of correlation squared. That is, R(2)=r(2)

1. True

2. False

 Objective: Interpret the results of a multiple regression.

 17. In explaining the income earned by college graduates, which of the following independent variables is best represented by a dummy variable?

1. Age

2. College major

3. Grade point average

4. Number of years since graduating from High School

 Week Five: Time Series and Forecasting Objective: Apply a time series analysis to forecast.

 18. Which of the following statements is true?

1. In trend analysis, the independent variable is time only if the equation is linear

2. The number of time periods in a centered moving average is always even.

3. If the seasonal index for December sales is 120, this means that December sales tend to be 120% as high as the "average" month.

4. The cyclical component of a time series refers to repeating patterns that have a period of a year or less.

 Objective: Make business decisions utilizing statistical and research outcomes.

 19. Forty samples of size 800 were drawn from a manufacturing process and the number of defectives in each sample was counted. The mean sample proportion was 0.035. The lower control limit for the p chart is

1. 0.0350.

2. 0.0155.

3. 0.0505.

4. 0.0545.

The questions contained in the Sample Examination and Final Examination were adapted from Applied Statistics in Business and Economics.

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