# Research methods, t-test, ANOVA, Chi-square

1. Select the best statistical analysis technique for the following research topics. Be very precise about your statistical choice. For example, there are several types of t tests, correlations, and ANOVA tests. Make sure you specify exactly which statistical analysis technique you would use, e.g. One-Way Anova.

a. You want to study regional differences (IV) in household savings (DV measured in dollars.) You randomly select samples of households in the West, South, and East.

b. You want to compare differences in sales dollars (DV) for 43 employees before and after they have attended a motivational seminar.

c. A sample of people is asked their height, and then a measurement of their height is taken. Your null hypothesis is that self-reported and actual heights (DV is height measured in inches) do not differ.

2. You wish to test the null hypothesis that gender (IV) makes no difference in purchasing one of four makes of cars (DV = Honda, Toyota, Lexus, Acura). Which statistical test would you conduct?

a. Re item 2, assume the critical value for this test is 4.92, and you obtain a computed statistical value of 7.45. Is there evidence to reject the null hypothesis?

3. You want to compare the effectiveness of three methods of teaching (IV). You plan to administer a standardized test (DV measured on an interval scale measuring knowledge acquisition) to the students in three classes with each class using a different teaching method.

a. State the research hypothesis you are testing.

b. What is the best method for assigning samples to test this hypothesis assuming you have absolute control over this experiment?

c. What statistical test would you use?

4. Your employer asks you to determine whether current salaries (DV) can be predicted from years of experience (IV).

a. What is the appropriate statistical test?

b. Referring back to item (a), if the computed statistical result is significant, what would you know?

c. You run a chi-square test. The critical value for this test at the .05 level is a chi-square of 6.21. What value must your obtained chi square statistic be in order to be considered significant at the .05 level?

5. A researcher wants to know if there is a relationship between a person's highest level of education (IV) and differences in life satisfaction (DV). She places her subjects into three samples (less than a high school degree, high school graduate, some college, or college degree). She creates a life satisfaction survey using a 4-point ordinal scale.

a. Would the Kruskal-Wallis be an appropriate statistical procedure to test this RQ? Please explain your answer.

b. When would you use the Chi-Square test rather than the Mann- Whitney U Test?

6. State a hypothesis that can be tested by: (Do not use examples from the lecture notes, QM, or textbooks. Create your own examples. Be very specific so that I can see you know the requirements for using each of these tests.)

a. One-way analysis of variance.

b. Simple regression.

c. Pearson correlation.

7. Briefly state what question you are trying to answer when you use simple regression. (Please use your own words.)

8. If you have simple regression output with one independent variable and the R-Square is .9332, what does the R-Square indicate?

9. The results of your correlation analysis show that you have a correlation of +.8932 between salary and productivity. What do you know?

10. Briefly, what is the difference between the static group comparison design and the posttest-only control group?

11. If your DV requires you to classify students by their major (e.g., accounting, human resources, health services, financial management, etc.), what type of measurement scale do you have?

12. Which type of measurement scale has the highest level of validity?

Answer the following multiple choice question:

13.

Source: http://www.psychstat.missouristate.edu/introbook/sbk27.htm

Sig. = Probability Value

Alpha Level = .05

F-critical = 2.76

The above ANOVA test displays the results of three different seminars (IV) each designed to improve self-concept (DV). From the data provided, were any of the seminars more effective than any of the others in improving self-concept?

a. No, there were no differences in the effectiveness of any of the seminars on improving self-concept.

b. Yes, all three seminars enhanced self-concept.

c. Yes, one of the seminars was significantly more effective than the other two.

14. A researcher wants to collect data about the study habits of sophomores at Harmond University. From the sophomore class of 2,300 students, she wants to collect a sample of 70 students. Which of the following sampling methods will yield the most representative sample?

a. Assigning each sophomore a number and then randomly generating 70 numbers from that list.

b. Randomly selecting 70 sophomores entering the university's main library on a randomly selected evening.

c. Selecting the 70 sophomores whose grade point averages (GPA) fall closest to the mean GPA of the sophomore class.

d. Randomly selecting 70 sophomores who are members of college fraternities.

15.

Hours Worked and Amount of Sales (in dollars)

Regression Statistics

Multiple R 0.9709

R2 0.9426

Adjusted R2 0.9394 F test results

Standard Error 1,889 F value Signif. F

Observations 20 295.51 0.0000

Coefficients Std Error t Stat P-value

Intercept 62,695 1,325 47.31 0.0000

Hours Worked 3,786 220 17.19 0.0000

Which of the following statements are true based on the statistical output featured above?

a. Hours worked is a significant predictor of amount of sales.

b. About 94% of amount of sales can be explained by hours worked.

c. Both a and b are true.

d. Neither a or b is true.

#### Solution Summary

The solution examines research methods, t-tests, ANOVA and chi-square analysis.