Question 1

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 17.894.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that 0.05 < p-value < 0.10.

Accepted Answer

Since the test statistic of 17.894 falls between the critical values of 6.251 and 18.307 for 10 degrees of freedom at the 0.01 level of significance, we know that the p-value must be greater than 0.01. However, it is less than the critical value of 23.209 at the 0.05 level of significance. Therefore, the most accurate statement we can make is that 0.05 < p-value < 0.10.

Question 2

It is known that the coefficients of skewness and kurtosis for the standard normal distribution are 0 and 3,respectively.

Accepted Answer

This statement is true. The standard normal distribution has a skewness coefficient of 0 and a kurtosis coefficient of 3. This is because the distribution is symmetric and has heavy tails compared to the normal distribution with a kurtosis of 0.

Question 3

The middle 0.90 portion of the chi-square distribution with 12 degrees of freedom has table values of 5.23 and 21.03,respectively.

Accepted Answer

This statement is true. The table values for the middle 0.90 portion of the chi-square distribution with 12 degrees of freedom are 5.23 and 21.03.

Question 4

In using the chi-square test for independence,one should be aware that the expected frequencies that are too small will lead to too big value of the probability of Type I error.

Accepted Answer

This is true. When the expected frequencies are too small, the chi-square distribution does not approximate the true distribution well, which can lead to an inflated probability of Type I error (rejecting the null hypothesis when it is true).

Question 5

The Mann-Whitney U test and the Wilcoxon rank test are only used for testing the medians for independent populations.

Accepted Answer

The Mann-Whitney U test and the Wilcoxon rank test are non-parametric tests used to compare the medians of two independent populations.

Question 6

A chi-square test for independence is applied to a contingency table with 3 rows and 4 columns for two qualitative variables.The degrees of freedom for this test must be 12.

Accepted Answer

The degrees of freedom for a chi-square test for independence with a contingency table that has 3 rows and 4 columns is (3-1)(4-1) = 6. Therefore, the correct answer is B.

Question 7

A chi-square test for independence is applied to a contingency table with 3 rows and 6 columns for two qualitative variables.The degrees of freedom for this test must be 10.

Accepted Answer

The degrees of freedom for a chi-square test for independence is calculated as (number of rows - 1) * (number of columns - 1). For a table with 3 rows and 6 columns, it is (3-1)*(6-1) = 2*5 = 10.

Question 8

A chi-square test for independence with 8 degrees of freedom results in a test statistic of 23.158.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that p-value > 0.005.

Accepted Answer

For a chi-square test with 8 degrees of freedom, a test statistic of 23.158 would correspond to a p-value less than 0.01 but greater than 0.005, indicating significant evidence against the null hypothesis at the 0.01 level but not at the 0.005 level.

Question 9

In order to examine whether a sample could have come from a given type of population distribution (e.g. ,Poisson or the normal distribution),chi-square analysis involves the comparison of a table of observed frequencies with a table of expected frequencies that has been constructed under the assumption that the null hypothesis is true.

Accepted Answer

This statement accurately describes the process of conducting chi-square analysis.

Question 10

A goodness-of-fit test features a table that classifies data with respect to two qualitative variables that are each divided into two or more categories;numbers in such a table show the frequency of occurrence of all possible combinations of categories.

Accepted Answer

A goodness-of-fit test is used to determine how well a set of observed frequencies fits a distribution of expected frequencies for a single categorical variable, not for the analysis of two qualitative variables in combination. The description given matches more closely with a contingency table analysis or a chi-square test of independence, which examines the relationship between two categorical variables.

Question 11

Nonparametric procedures have fewer restrictive assumptions concerning data level and underlying probability distributions.

Accepted Answer

Nonparametric procedures do not assume normality or other specific underlying probability distributions, making them more flexible than parametric procedures.

Question 12

The middle 0.95 portion of the chi-square distribution with 9 degrees of freedom has table values of 3.325 and 16.919,respectively.

Accepted Answer

The answer of The middle 0.95 portion of the chi-square...

Question 13

For tests of independence,the expected frequencies depend only on the sample size.

Accepted Answer

The expected frequencies in tests of independence, such as the Chi-square test, depend on both the sample size and the marginal totals of the rows and columns in the contingency table.

Question 14

A chi-square test for independence is applied to a contingency table with 4 rows and 4 columns for two qualitative variables.The degrees of freedom for this test must be 9.

Accepted Answer

The degrees of freedom for a chi-square test for independence in a contingency table is calculated as (number of rows - 1) * (number of columns - 1), which in this case is (4-1)*(4-1) = 3*3 = 9.

Question 15

The Mann-Whitney U test and Wilcoxon rank sum test are equivalent to each other.

Accepted Answer

The Mann-Whitney U test and Wilcoxon rank sum test both compare two independent groups and test for differences in location (i.e. median). They are different names for the same test.

Question 16

When the parameters of the distribution of interest are not specified and must be estimated,the chi-square test statistic always loses 2 or more degrees of freedom.

Accepted Answer

The loss in degrees of freedom for a chi-square test statistic depends on the number of parameters estimated from the data; typically, one degree of freedom is lost for each parameter estimated.

Question 17

In a normal approximation to the sign test,the standardized test statistic is calculated as z = 2.17.If the alternative hypothesis states that the location of population 1 is to the right of the location of population 2,then the p-value of the test is 0.015.

Accepted Answer

This is true because a z-statistic of 2.17 corresponds to a p-value of approximately 0.015 when using a normal distribution. Since the alternative hypothesis states that population 1 is to the right of population 2, this is a one-tailed test and the p-value is in the right tail of the distribution. Therefore, a p-value of 0.015 indicates that the observed data is unlikely to have occurred by chance and we reject the null hypothesis in favor of the alternative hypothesis.

Question 18

The cells in the contingency table reflect the responses to each combination of categories for the variables of interest.

Accepted Answer

This statement is true. A contingency table displays the frequencies or counts of observations within each combination of categories for two or more categorical variables. The cells in the contingency table represent the number of individuals or objects that fall into each combination of categories, which can be used to compute various statistics such as percentages, proportions, and odds ratios.

Question 19

The number of degrees of freedom for a contingency table with r rows and c columns is equal to rc,provided that both r and c are greater than or equal to 2.

Accepted Answer

The number of degrees of freedom for a contingency table with r rows and c columns is equal to (r-1)(c-1), not rc. This is because the last row and column can be determined from the other rows and columns, so they are not independent.

Question 20

The test statistic for the Jarque-Bera test for normality does not depend on the sample size.

Accepted Answer

The Jarque-Bera test statistic depends on both skewness and kurtosis, which are calculated from the sample data. As the sample size increases, the estimates of skewness and kurtosis become more accurate, affecting the test statistic.

Quiz 14: Analysis of Categorical Data