Question 1

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

Accepted Answer

The expected frequencies in a chi-square test of independence are calculated based on the assumption that there is no association between the two variables being tested, which is the null hypothesis. These expected frequencies are then compared to the observed frequencies to determine if there is a significant relationship between the variables.

Question 2

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

This statement is true. The chi-square goodness of fit test with multinomial probabilities tests the hypothesis that the observed frequencies in each category are consistent with the expected frequencies based on the specified multinomial probabilities. If the null hypothesis is rejected, it means that at least one of the multinomial probabilities is not equal to the specified value.

Question 3

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

Accepted Answer

The χ² goodness of fit test is used for nominal data, so it requires the nominative level of data.

Question 4

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

Accepted Answer

As the difference between observed and expected frequencies decreases, the chi-square statistic becomes smaller, increasing the probability of concluding that the variables are independent.

Question 5

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 alternative hypothesis, we state that the two classifications are not statistically independent.

Question 6

When we carry out a chi-square test of independence,the chi-square statistic is based on (rc - 1)degrees of freedom,where r and c denote,respectively,the number of rows and columns in the contingency table.

Accepted Answer

The degrees of freedom formula for a chi-square test of independence is (r-1)(c-1), not (rc-1).

Question 7

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

Accepted Answer

A multinomial experiment involves multiple trials where each trial has two or more possible outcomes. Therefore, the resulting data can be classified into two or more categories, which is described by a multinomial probability distribution.

Question 8

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

This is the correct formula for estimating the expected cell frequency in a chi-square test of independence.

Question 9

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

If the value of the chi-square statistic is large enough, it indicates that the observed data differs significantly from the expected data based on the null hypothesis. Therefore, we reject the null hypothesis and conclude that there is a statistical difference between the observed and expected data.

Question 10

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 applied to test if a sample data comes from other distribution forms such as the Poisson.

Accepted Answer

The statement is incorrect. The chi-square goodness of fit test can be used to test the fit of the sample data to any specified distribution, including the Poisson distribution.

Question 11

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

Accepted Answer

A contingency table presents the frequencies and/or percentages of observations that fall into various categories for two variables.

Question 12

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 at least approximately normally distributed.

Accepted Answer

Rejecting the null hypothesis of a chi-square goodness-of-fit test does not necessarily imply that the population is normally distributed. It only means that the observed distribution of data is significantly different than the expected distribution assumed by the null hypothesis. There could be other distributions that fit the observed data better.

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

The actual counts in the cells of a contingency table are referred to as the observed cell frequencies, while the expected cell frequencies are the counts that would be expected if there were no association between the variables.

Question 15

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 16

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

Accepted Answer

This is true. When all the expected frequencies are equal to the observed frequencies, the calculated χ² statistic will be zero.

Question 17

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

Accepted Answer

Trials of a multinomial probability are assumed to be independent.

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

This is a correct use of the chi-square goodness of fit test.

Question 20

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 correct.

Accepted Answer

This is because the chi-square test statistic measures the discrepancy between observed and expected frequencies, and a smaller difference between them would result in a smaller value for the test statistic, making it less likely to reject the null hypothesis.

Quiz 13: Chi-Square Tests