Question 1

A multinomial probability distribution describes data that are classified into two or more categories when a multinomial experiment is carried out.

Accepted Answer

They are similar to the one that defines a binomial experiment (where K = 2).

Question 2

A fastener manufacturing company uses a chi-square goodness-of-fit test to determine if a population of all lengths of ¼-inch bolts it manufactures is distributed according to a normal distribution. If we reject the null hypothesis, it is reasonable to assume that the population distribution is approximately normally distributed.

Accepted Answer

If the null hypothesis is rejected, then the population does not have a normal distribution.

Question 3

The chi-square goodness-of-fit test can only be used to test whether a population has specified multinomial probabilities or to test if a sample has been selected from a normally distributed population. It cannot be used if sample data come from other distribution forms, such as the Poisson.

Accepted Answer

The chi-square goodness-of-fit test can be used to test sample data from other distribution forms.

Question 4

When we carry out a chi-square test of independence, the expected frequencies are based on the null hypothesis.

Accepted Answer

The expected frequencies are the frequencies you would expect to see under the null hypothesis, so you want there to be a large difference between the observed and the expected in order to have a chance at rejecting the null hypothesis.

Question 5

The χ² goodness-of-fit test requires the nominative level of data.

Accepted Answer

The results of the experiment are observed frequencies (counts) and the number of trials that result in each of the possible outcomes.

Question 6

One use of the chi-square goodness-of-fit test is to determine if specified multinomial probabilities in the null hypothesis are favored over the alternative hypothesis.

Accepted Answer

The more the observed frequencies differ from the expected frequencies, the larger chi-square will be and the more doubt will be cast on the null hypothesis.

Question 7

In a contingency table, if all of the expected frequencies equal the observed frequencies, then we can conclude that there is a perfect association between rows and columns.

Accepted Answer

Conclusion is that the rows and columns are statistically independent.

Question 8

The actual counts in the cells of a contingency table are referred to as the expected cell frequencies.

Accepted Answer

Actual counts in the cells are referred to as observed cell frequencies.

Question 9

When we carry out a chi-square test of independence, in the alternative hypothesis we state that the two classifications are statistically independent.

Accepted Answer

In the chi-square test of independence, the null hypothesis is that the two classifications are independent.

Question 10

When using a chi-square goodness-of-fit test with multinomial probabilities, the rejection of the null hypothesis indicates that at least one of the multinomial probabilities is not equal to the value stated in the null hypothesis.

Accepted Answer

It does not tell you exactly which one, but you know at least one of the probabilities is not equal to the value in the null hypothesis.

Question 11

In a contingency table, when all the expected frequencies equal the observed frequencies, the calculated χ² statistic equals zero.

Accepted Answer

That means that there is no difference in what you expected to see and what you truly did see in the data.

Question 12

A contingency table summarizes data that has been classified into two dimensions or scales.

Accepted Answer

It is particularly helpful when dealing with categorical data.

Question 13

The trials of a multinomial probability are assumed to be dependent.

Accepted Answer

Trials of a multinomial probability are assumed to be independent.

Question 14

In performing a chi-square test of independence, as the difference between the respective observed and expected frequencies calculated by assuming independence decreases, the probability of concluding that the row variable is independent of the column variable decreases.

Accepted Answer

When a chi-square test for independence is large (observed frequencies differ substantially from the expected frequencies), then doubt will be cast on the null hypothesis of independence. Therefore, a small chi-square would result in a larger probability.

Question 15

In performing a chi-square goodness-of-fit test with multinomial probabilities, the smaller the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are favored over the alternative hypothesis.

Accepted Answer

If there is very little difference between the observed frequencies and the calculated frequencies, there is a very small chance that you will reject the null hypothesis.

Question 16

When using the chi-square goodness-of-fit test, if the value of the chi-square statistic is large enough, we reject the null hypothesis.

Accepted Answer

The larger the chi-square value, the higher the probability we will reject the null hypothesis.

Question 17

The chi-square distribution is a continuous probability distribution that is skewed to the left.

Accepted Answer

Chi-square distribution is skewed to the right.

Question 18

When we carry out a chi-square test of independence, if r_i is the row total for row i and c_j is the column total for column j, then the estimated expected cell frequency corresponding to row i and column j equals (r_i)(c_j)/n.

Accepted Answer

Where n is the total number of observed frequencies.

Question 19

When we carry out a chi-square test of independence, the chi-square statistic is based on  degrees of freedom, where r and c denote, respectively, the number of rows and columns in the contingency table.

Accepted Answer

Degrees of freedom = (r − 1)(c − 1).

Question 20

Expected cell frequencies for a multinomial distribution are calculated by assuming statistical dependence.

Accepted Answer

Expected cell frequencies are calculated by assuming statistical independence.

Quiz 13: Chi-Square Tests