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# Chi-square Test & Correlation Coefficient

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1. Use the contingency table below to determine if there is evidence of a significant difference between proportions of males and females who enjoy shopping for clothing at the 0.01 level of significance. Determine the p-value in (a) and interpret its meaning.

Yes No Total
Males 136 104 240
Females 224 36 260
Total 360 140 500

2. Football players trying out for the NFL are given the Wonderlic intelligence test. The data below contains the average Wonderlic score of those players and the graduation rates for football players at selected schools. Compute the covariance and the coefficient of correlation. What conclusions can you reach about the relation between average Wonderlic score and graduation rate?
Stanford 28.8 85
Purdue 25.3 63
California 25.2 48
UCLA 24.0 55
Oregon 23.5 68
Wisconsin 23.2 56
Iowa 23.0 58
Oregon State 22.8 44
Notre Dame 22.5 77
Boston College 22.0 78
Michigan 21.7 57
Virginia 21.5 75
Texas A & M 21.0 50
Florida 20.8 42
Ohio State 20.8 52
Penn State 20.7 74
Virginia Tech 20.7 58
Southern California 20.3 58
West Virginia 20.3 46
Arizona State 20.2 44
Kansas State 19.8 61
Georgia 19.8 53
Texas 19.7 34
North Carolina State 19.6 42
Florida State 19.4 49
Oklahoma 19.0 40
North Carolina 18.9 53
Arkansas 18.6 35
Auburn 18.5 48
LSU 18.5 42
Clemson 18.3 51
Alabama 18.2 49
South Carolina 17.9 54
Tennessee 17.7 38
Michigan State 16.6 41
Miami (Florida) 16.3 57

https://brainmass.com/statistics/correlation-and-regression-analysis/chi-square-test-correlation-coefficient-601350

#### Solution Summary

The solution provides a step by step method for the calculation of chi square test for association and correlation coefficient. Formula for the calculation and interpretation of the results are also included.

\$2.19

## Statistic problems

1. What information is provided by the numerical value of the Pearson correlation?

2. In the following data, there are three scores (X, Y, and Z) for each of the n= 5 individuals:

X Y Z

3 5 5

4 3 2

2 4 6

1 1 3

0 2 4

a. Sketch a graph showing the relationship between X and Y. Compute the Pearson correlation between X and Y.
b. Sketch a graph showing the relationship between Y and Z. Compute the Pearson correlation Between Y and Z.
c. Given the results of parts a and b, what would you predict for the correlation between X and Z?
d. Sketch a graph showing the relationship between X and Z. Compute the Pearson correlation for these data.
e. What general conclusion can you make concerning relationships among correlations? If X is related to Y and Y is related to Z, does this necessarily mean that X is related to Z?

3. For each of the following, determine whether the sample provides enough evidence to conclude that there is a significant, nonzero correlation in the population. In each case, use a two-tailed test with x = .05.

a. A sample of n = 18 with r = -0.50
b. A sample of n = 15 with r = -.0.50.
c. A sample of n = 30 with r = 0.275
d. A sample of n = 25 with r = 0.375

4. A professor noticed that the representatives on the college student government consist of 31 males and only 9 females. The general college population, on the other hand, consists of 55% females and 45% males. Is the gender distribution for student from the distribution for the college population? Test at the .05 level of significance.

5. A researcher obtained a random sample of n = 60students to determine whether there were any significant preferences among three leading brands of colas. Each student tasted all three brands and then selected his or her favorite. The resulting frequency distribution is as follows:

Brand A Brand B Brand C
28 14 18

6. A social psychologist suspects that people who serve on juries tend to be much older than citizens in the general population. Jurors are selected from the list of registered voters, so the ages for jurors should have the same distribution as the ages for voters. The psychologist obtains voter registration records and finds that 20% of registered voters are between 18 and 29 years old, 45% are between 30 and 49 years old, and 35% are age 50 or older. The psychologist also monitors jury composition over several weeks and observes the following distribution of ages for actual juries:

Age Categories for Jurors

18-29 30-49 50 and over
12 36 32

Are the data sufficient to conclude that the age distribution for jurors is significantly different from the distribution for the population of registered voters?
Test with X = .05.