**test 3 AA**

**Multiple Choice**

*Identify the choice that best completes the statement or answers the question.*

____ 1. For an ANOVA comparing three treatment conditions, what is stated by the alternative hypothesis (H_{1})?

a. | There are no differences between any of the population means. |

b. | At least one of the three population means is different from another mean. |

c. | All three of the population means are different from each other. |

d. | None of the other choices is correct. |

____ 2. On average, what value is expected for the F-ratio if the null hypothesis is true?

a. | 0 | c. | k – 1 |

b. | 1.00 | d. | N – k |

____ 3. A research study comparing three treatments with *n* = 5 in each treatment produces T_{1} = 5, T_{2} = 10, T_{3} = 15, with SS_{1} = 6, SS_{2} = 9, SS_{3} = 9, and SX^{2 }= 94. For this study, what is SS_{between}?

a. | 10 | c. | 34 |

b. | 24 | d. | 68 |

____ 4. An analysis of variance produces SS_{between} = 30, SS_{within } = 60, and an F-ratio with df = 2, 15. For this analysis, what is the F-ratio?

a. | 30/60 = 0.50 | c. | 15/4 = 3.75 |

b. | 60/30 = 2.00 | d. | 4/15 = 0.27 |

____ 5. If an analysis of variance is used for the following data, what would be the effect of changing the value of M_{1} to 20?

__Sample Data__

M_{1} = 15 M_{2} = 25

SS_{1} = 90 SS_{2} = 70

a. | Increase SS_{between} and increase the size of the F-ratio |

b. | Increase SS_{between} and decrease the size of the F-ratio |

c. | Decrease SS_{between} and increase the size of the F-ratio |

d. | Decrease SS_{between} and decrease the size of the F-ratio |

____ 6. In general, what factors are most likely to reject the null hypothesis for an ANOVA?

a. | Small mean differences and small variances |

b. | Small mean differences and large variances |

c. | Large mean differences and small variances |

d. | Large mean differences and large variances |

____ 7. A two-factor study with two levels of factor A and three levels of factor B uses a separate group of *n* = 5 participants in each treatment condition. How many participants are needed for the entire study?

a. | 5 | c. | 25 |

b. | 10 | d. | 30 |

____ 8. The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. What value for the missing mean would result in no A´B interaction?

B1 B2

A1 |
20 |
30 |

A2 |
10 |
? |

a. | 10 | c. | 30 |

b. | 20 | d. | 40 |

____ 9. If a two-factor analysis of variance produces a statistically significant interaction, what can you conclude about the main effects?

a. | Either the main effect for factor A or the main effect for factor B is also significant |

b. | Both the man effect for factor A and the main effect for factor B are significant |

c. | Neither the main effect for factor A nor the main effect for factor B is significant |

d. | The significance of the main effects is not related to the significance of the interaction |

____ 10. What is indicated by a positive value for a correlation?

a. | Increases in X tend to be accompanied by increases in Y |

b. | Increases in X tend to be accompanied by decreases in Y |

c. | A much stronger relationship than if the correlation were negative |

d. | A much weaker relationship than if the correlation were negative |

____ 11. The scatter plot for a set of X and Y values shows the data points clustered in a nearly perfect circle. For these data, what is the most likely value for the Pearson correlation?

a. | A positive correlation near 0 | c. | Either positive or negative near 0 |

b. | A negative correlation near 0 | d. | A value near +1.00 or -1.00 |

____ 12. What is indicated by a Pearson correlation of r = +1.00 between X and Y?

a. | Each time X increases, there is a perfectly predictable increase in Y |

b. | Every change in X causes a change in Y |

c. | Every increase in X causes an increase in Y |

d. | All of the other 3 choices occur with a correlation of +1.00. |

____ 13. What is the value of SP for the following set of data?

X | Y |

4 | 3 |

1 | 2 |

1 | 5 |

2 | 6 |

______________

____ 14. Suppose the correlation between height and weight for adults is +0.40. What proportion (or percent) of the variability in weight can be explained by the relationship with height?

a. | 40% | c. | 16% |

b. | 60% | d. | 84% |

____ 15. As the sample size gets larger, what happens to the size of the correlation that is needed for significance?

a. | It also gets larger |

b. | It gets smaller |

c. | It stays constant |

d. | There is no consistent relationship between sample size and the critical value for a significant correlation. |

____ 16. Under what circumstances is the phi-coefficient used?

a. | When one variable consists of ranks and the other is regular, numerical scores |

b. | When both variables consists of ranks |

c. | When both X and Y are dichotomous variables |

d. | When one variable is dichotomous and the other is regular, numerical scores |

____ 17. A set of X and Y scores has M_{X} = 4, SS** _{X}** = 10, M

_{Y}= 5, SS

**= 40, and SP = 20. What is the regression equation for predicting Y from X?**

_{Y}a. | c. | ||

b. | d. |

____ 18. A linear regression equation has b = 3 and a = – 6. What is the predicted value of Y for X = 4?

a. | |

b. | |

c. | |

d. | Cannot be determined without additional information |

____ 19. A set of *n* = 25 pairs of scores (X and Y values) has a Pearson correlation of r = 0.80. How much of the variance for the Y scores is predicted by the relationship with X?

a. | 0.36 or 36% | c. | 0.80 or 80% |

b. | 0.20 or 20% | d. | 0.64 or 64% |

____ 20. Which of the following best describes the possible values for a chi-square statistic?

a. | Chi-square is always a positive whole numbers. |

b. | Chi-square is always positive but can contain fractions or decimal values. |

c. | Chi-square can be either positive or negative but always is a whole number. |

d. | Chi-square can be either positive or negative and can contain fractions or decimals. |

____ 21. What conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?

a. | There is a good fit between the sample data and the null hypothesis. |

b. | There is a large discrepancy between the sample data and the null hypothesis. |

c. | All of the expected frequencies must also be close to zero. |

d. | The researcher made a mistake because chi-square can never be close to zero. |

____ 22. A researcher is using a chi-square test to determine whether people have any preferences among three brands of televisions. The null hypothesis for this test would state that ______.

a. | there are real preferences in the population |

b. | one-third of the sample prefers each brand |

c. | one-third of the population prefers each brand |

d. | in the population, one brand is preferred over the other two |

____ 23. A sample of 100 people is classified by gender (male/female) and by whether or not they are registered voters. The sample consists of 80 females and 20 males, and has a total of 60 registered voters. If these data are used for a chi-square test for independence, what is the total number of females for the expected frequencies?

a. | 32 | c. | 48 |

b. | 20 | d. | 80 |

____ 24. A researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and registering to vote. The sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters. If these data were used for a chi-square test for independence, what is the observed frequency for registered males?

a. | 12 | c. | 40 |

b. | 28 | d. | 42 |

**Short Answer**

- A psychologist would like to examine the effects of different testing methods on the final performance of college students. One group gets regular quizzes, one group gets three large exams, and the third group only gets a final exam. At the end of the course, the psychologist interviews each student to get a measure of the student’s overall knowledge of the material.

**Please show your manual calculations**

- Do these data indicate any significant differences among the three methods? Test with
*á*= .05. - Compute Tukey’s HSD to determine exactly which methods are significantly different.

Quizzes | Exams | Final Only | |

4 | 1 | 0 | |

6 | 4 | 2 | |

3 | 5 | 0 | |

7 | 2 | 2 | |

- Compute the Pearson correlation for the following data.
**Please show your manual calculations**

X | Y |

2 | 3 |

3 | 1 |

6 | 5 |

4 | 4 |

5 | 2 |

- A researcher is examining preferences among four new flavors of ice cream. A sample of
*n*= 80 people is obtained. Each person tastes all four flavors and then picks his/her favorite. The distribution of preferences is as follows.

Ice Cream Flavor

A B C D

12 |
18 |
28 |
22 |

Do these data indicate any significant preferences among the four flavors? Test at the .05 level of significance.

- A researcher would like to know whether there is a consistent, predictable relationship between verbal skills and math skills for high school students. A sample of 200 students is obtained, and each student is given a standardized English test and a standardized math test. Based on the test results, students are classified as high or low for verbal skills and for math skills. The results are summarized in the following frequency distribution:

Verbal Skills

High Low

High Math |
59 | 41 |

Low Math | 31 | 69 |

- Based on these results, can the researcher conclude that there is a significant relationship between verbal skills and math skills? Test at the .05 level of significance.
- Compute the phi-coefficient to measure the strength of the relationship.

29 A researcher is interested in the relationship between GPA and Sorority/Fraternity membetrship. She conducted a study with 5 soroity women and 5 non sorority women. She also included 5 male in a fraternity and five males who were not members of a fraternity. She gathered the GPS’s of each and analyzed using spss, which produced the following tables:

Cell Means

Gender

Female Male

Member 3.3 3.1

Non-member 3.6 3.4

Tests of Between Subjects Effects

Source Type III Sum Squares df Mean Square F Sig

Gender 500 1 500 2.0 .35

Member 1000 1 1000 5.6 .045

Gender*member 250 1 250 3.5 .89

Error 3300 200

FIRST draw a LINE GRAPH showing CELL MEANS

SECOND Interpret the results table of Between Subjects Effects. That is, Were there any main effects

or interaction effects, AND why do you say that.