For sample sizes that are very small, it is possible for the chi-square statistic to have value that

Select True or False

1. For sample sizes that are very small, it is possible for the chi-square statistic to have value that is negative.

2. The chi-square distribution is a family of distributions, with a different curve for each possible value for the number of degrees of freedom.

3. The chi-square distribution is a discrete distribution,

4. The number of degrees of freedom in a chi-square test refers to the number of values free to vary once some information about all of the values is already known.

5. Chi-square analysis can be used in examining whether a sample could have come from a

6. In using chi-square for testing the independence of variables, the table of observed frequencies is constructed under the assumption that the null hypothesis is true.

7. In using chi-square for testing the independence of variables, larger calculated values for chi-square will tend to make it more likely that the null hypothesis will be rejected.

8. A contingency table for two nominal variables has three (3) row and four (4) columns. The number of degrees of freedom associated with the chi-square test of variable independence will be df= 6.

9. In carrying out chi-square analysis, if one or more of the observed frequencies is less than five (5), rows or columns should be combined so that each value of O_ijis at least 5.

Multiple Choice

1. In a chi-square testing of the independence of two nominal-scale variables, the first variable has 4 different categories, and the second variable has 3 different categories. How many degrees of freedom will be associated with the test?

1. 12

2. 3

3. 6

4. 7

1. In testing the independence of two nominal variables, the critical; value of chi-square is 5.991 for the 0.05 level. If the test were at the 0.01 level, the critical value would be

1. Greater than 5.991

2. Less than 5.991

3. Equal to 5.991

4. Not enough information has been provided.

1. In examining whether a sample could have been drawn from a normal distribution, the appropriate chi-square test would be the

1. Test for independence

2. Test for goodness-of-fit

3. Test for equal proportion

4. Test for the population variance

A survey was conducted to determine student, faculty and administration attitudes on a new university parking facility. The distribution of respondents is given below:

1. Determine the X² value for row 1 and column 2

1. 0.14

2. 1.55

3. 1.24

4. 0.35

1. Determine the expected frequency for row 1 and column 2

   1. 27.37

   2. 28.50

   3. 28.37

   4. 27.63

2. What is the null hypothesis for a chi-square test of association

1. There is difference between the populations

2. There is a relationship between the two variables

3. There is no difference between the populations

4. There is no relationship between the two variables

1. Chi square test are

1. One tail tests

2. Tests of proportions

3. Test of independence and goodness of fit

4. Two tail tests

1. The chi square distribution is

1. Symmetrical

2. Positively skewed

3. Negatively skewed

4. None of the above

1. Given a 4x7 contingency table, what are the degrees of freedom?

1. 10

2. 19

3. 18

4. 15