# Using t test, chi square test and Wilconxon rank sum test

2. A student is interested in whether students who study with music playing devote as much attention to their studies as do students who study under quiet conditions (he believes that studying under quiet conditions leads to better attention). He randomly assigns participants to either the music or no- music condition and has them read and study the same passage of information for the same amount of time. Subjects are given the same 10- item test on the material. Their scores appear next. Scores on the test represent interval- ratio data and are normally distributed.

Music No Music

6 10

5 9

6 7

5 7

6 6

6 6

7 8

8 6

5 9

a. What statistical test should be used to analyze these data?.

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

e. If significant, compute and interpret the effect size.

f. If significant, draw a graph representing the data.

g. Determine the 95% confidence interval.

4. The researcher in exercise 2 decides to conduct the same study using a within- participants design to control for differences in cognitive ability. He selects a random sample of subjects and has them study different material of equal difficulty in both the music and no- music con-ditions. The study is completely counterbalanced to control for order effects. The data appear next. As before, they are measured on an interval- ratio scale and are normally distributed; he believes that studying under quiet conditions will lead to better performance.

Music No Music

7 7

6 8

5 7

6 7

8 9

8 8

a. What statistical test should be used to analyze these data?

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

e. If significant, compute and interpret the effect size.

f. If significant, draw a graph representing the data.

6. Researchers at a food company are interested in how a new spaghetti sauce made from green tomatoes (and green in color) will compare to their traditional red spaghetti sauce. They are worried that the green color will adversely affect the tastiness scores. They randomly assign subjects to either the green or red sauce condition. Participants indicate the tastiness of the sauce on a 10- point scale. Tastiness scores tend to be skewed. The scores follow.

Red Sauce Green Sauce

7 4

6 5

9 6

10 8

6 7

7 6

8 9

a. What statistical test should be used to analyze these data?

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

8. You notice in your introductory psychology class that more women tend to sit up front, and more men sit in the back. To determine whether this difference is significant, you collect data on the seating preferences for the students in your class. The data follow.

Men Women

Front of the Room 15 27

Back of the Room 32 19

a. What is 2obt?

b. What is df for this test?

c. What is 2 cv?

d. What conclusion should be drawn from these results?

https://brainmass.com/statistics/students-t-test/test-chi-square-test-wilconxon-rank-sum-test-612630

#### Solution Preview

2. A student is interested in whether students who study with music playing devote as much attention to their studies as do students who study under quiet conditions (he believes that studying under quiet conditions leads to better attention). He randomly assigns participants to either the music or no- music condition and has them read and study the same passage of information for the same amount of time. Subjects are given the same 10- item test on the material. Their scores appear next. Scores on the test represent interval- ratio data and are normally distributed.

Music No Music

6 10

5 9

6 7

5 7

6 6

6 6

7 8

8 6

5 9

a. What statistical test should be used to analyze these data?.

Since two samples are independent, we use t test for two independent samples.

b. Identify H0 and Ha for this study.

Let u1 and u2 be mean score for music and no music groups.

Ho: u1=u2

Ha: u1<u2

c. Conduct the appropriate analysis.

Let group 1 be music group and group 2 be no music group.

So xbar1=6, sd1=1, xbar2=7.5556, sd2=1.5092.

So test statistic=(6-7.5556)/sqrt[12/9+1.50922/9]=-2.5777

d. Should H0 be rejected? What should the researcher conclude?

At df=9+9-2=16, at 0.05 level, from t table, the critical value is -1.746.

Since -1.746>-2.5777, we ...

#### Solution Summary

The solution gives detailed steps on solving some questions using t test, chi square test and Wilconxon rank sum test.