Chapter 14 Goodness of fit tests and categorical data analysis
COMPLETION
1. A generalizes a binomial experiment by allowing each trial to result in one of k possible outcomes
(categories), where k > 2.
ANS: multinomial experiment
PTS: 1
2. The chi-squared distribution has a single parameter , called the number of the distribution.
ANS: degrees of freedom
PTS: 1
3. The critical value for the chi-squared distribution is the value such that of the area under the
curve with degrees of freedom lies to the right of
ANS: .05
PTS: 1
4. Provided that for every i (i =1, 2, 3, 4, 5), the goodness-of-fit test statistic when category probabilities are
completely specified has approximately a chi-squared distribution with degrees of freedom.
, ANS: 4
PTS: 1
5. If Z is a standard normal random variable; that is , then has a distribution with degrees
of freedom = .
ANS: chi-squared, 1
PTS: 1
6. The area to the right of 4.93 under the 2 degrees of freedom chi-squared curve is .
ANS: .085
PTS: 1
7. One may wish to test is not true. The null hypothesis is
hypothesis in the sense that each is a specified number, so that the expected cell counts when is true are
uniquely determined numbers.
ANS: simple
PTS: 1
8. One may wish to test is not true. The null hypothesis
is hypothesis because knowing that is true does not uniquely determine the cell probabilities and
expected cell counts but only their general form.
ANS: composite
PTS: 1
9. The goodness-of-fit test statistics, when there are 6 categories and 2 parameters to be estimated, has approximately
a chi-squared distribution with degrees of freedom.
ANS: 3
PTS: 1
10. If the computed value of the chi-squared test statistic is =2.83, and the test has 2 degrees of freedom, then the null
hypothesis is at .05 level of significance.
ANS: not rejected
PTS: 1
11. It is true that the more the sample correlation coefficient r deviates from , the less the normal probability
plot resembles a straight line.
, ANS: 1
PTS: 1
12. In a two-way contingency table, if the second row total is 125, the third column total is 60, and the total number of
observations is 375, then the estimated expected count in cell (2, 3) is .
ANS: 20
PTS: 1
13. A two-way contingency table has 3 rows and 5 columns. Then, the number of degrees of freedom associated with the
chi-squared test for homogeneity is .
ANS: 8
PTS: 1
14. The chi-squared test for homogeneity can safely be applied as long as the estimated expected count is at least
for all cells.
ANS: 5
PTS: 1
15. A two-way contingency table has r rows and c columns. Then, the number of degrees of freedom associated with the
chi-squared test for independence is .
ANS: (r-1)(c-1)
PTS: 1
MULTIPLE CHOICE
1. Which of the following statements are not true?
a. The chi-squared distribution is used to obtain a confidence interval for the variance of a normal
population.
b. Provided that for every i (i =1, 2,……, k), the goodness-of-fit test statistic when all k
category probabilities are completely specified has approximately a t distribution with k-1 degrees
of freedom.
c. A multinomial experiment generalizes a binomial experiment by allowing each trial to result in one
of k possible outcomes, where k>2. In general, we refer to these outcomes as categories.
d. All of the above statements are correct.
e. None of the above statements are correct.
ANS: B PTS: 1
2. Which of the following statements are true regarding the critical value for the chi-squared distribution when
COMPLETION
1. A generalizes a binomial experiment by allowing each trial to result in one of k possible outcomes
(categories), where k > 2.
ANS: multinomial experiment
PTS: 1
2. The chi-squared distribution has a single parameter , called the number of the distribution.
ANS: degrees of freedom
PTS: 1
3. The critical value for the chi-squared distribution is the value such that of the area under the
curve with degrees of freedom lies to the right of
ANS: .05
PTS: 1
4. Provided that for every i (i =1, 2, 3, 4, 5), the goodness-of-fit test statistic when category probabilities are
completely specified has approximately a chi-squared distribution with degrees of freedom.
, ANS: 4
PTS: 1
5. If Z is a standard normal random variable; that is , then has a distribution with degrees
of freedom = .
ANS: chi-squared, 1
PTS: 1
6. The area to the right of 4.93 under the 2 degrees of freedom chi-squared curve is .
ANS: .085
PTS: 1
7. One may wish to test is not true. The null hypothesis is
hypothesis in the sense that each is a specified number, so that the expected cell counts when is true are
uniquely determined numbers.
ANS: simple
PTS: 1
8. One may wish to test is not true. The null hypothesis
is hypothesis because knowing that is true does not uniquely determine the cell probabilities and
expected cell counts but only their general form.
ANS: composite
PTS: 1
9. The goodness-of-fit test statistics, when there are 6 categories and 2 parameters to be estimated, has approximately
a chi-squared distribution with degrees of freedom.
ANS: 3
PTS: 1
10. If the computed value of the chi-squared test statistic is =2.83, and the test has 2 degrees of freedom, then the null
hypothesis is at .05 level of significance.
ANS: not rejected
PTS: 1
11. It is true that the more the sample correlation coefficient r deviates from , the less the normal probability
plot resembles a straight line.
, ANS: 1
PTS: 1
12. In a two-way contingency table, if the second row total is 125, the third column total is 60, and the total number of
observations is 375, then the estimated expected count in cell (2, 3) is .
ANS: 20
PTS: 1
13. A two-way contingency table has 3 rows and 5 columns. Then, the number of degrees of freedom associated with the
chi-squared test for homogeneity is .
ANS: 8
PTS: 1
14. The chi-squared test for homogeneity can safely be applied as long as the estimated expected count is at least
for all cells.
ANS: 5
PTS: 1
15. A two-way contingency table has r rows and c columns. Then, the number of degrees of freedom associated with the
chi-squared test for independence is .
ANS: (r-1)(c-1)
PTS: 1
MULTIPLE CHOICE
1. Which of the following statements are not true?
a. The chi-squared distribution is used to obtain a confidence interval for the variance of a normal
population.
b. Provided that for every i (i =1, 2,……, k), the goodness-of-fit test statistic when all k
category probabilities are completely specified has approximately a t distribution with k-1 degrees
of freedom.
c. A multinomial experiment generalizes a binomial experiment by allowing each trial to result in one
of k possible outcomes, where k>2. In general, we refer to these outcomes as categories.
d. All of the above statements are correct.
e. None of the above statements are correct.
ANS: B PTS: 1
2. Which of the following statements are true regarding the critical value for the chi-squared distribution when
