Question 1

The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated minus one.

Accepted Answer

This statement is true. The formula for degrees of freedom in a chi-square goodness-of-fit test is (# of categories - # of parameters estimated - 1), where the parameters estimated include any constants or variables estimated from the data. This statement is true. The formula for calculating the degrees of freedom in a chi-square goodness-of-fit test is df = k - s - 1, where k is the number of categories and s is the number of parameters estimated from the data.

Question 2

When using the chi-square goodness-of-fit test, we must make sure that none of the expected frequencies is less than 30.

Accepted Answer

The rule of thumb for the chi-square goodness-of-fit test is that none of the expected frequencies should be less than 5, not 30. If any expected frequency is less than 5, the test may not be valid and an alternative test should be considered.

Question 3

A two-way table used for a test of independence is sometimes called a contingency table.

Accepted Answer

A contingency table is a two-way table used to determine whether there is a relationship between two categorical variables. It is commonly used in tests of independence, such as chi-squared tests. This is correct. A two-way table used for a test of independence is also known as a contingency table, which displays the frequencies or counts of two categorical variables.

Question 4

A chi?square goodness-of-fit test is being used to test the goodness-of-fit of a normal distribution (the mean and the standard deviation of which must be estimated)for a data with "k" categories.This test has (k-3)degrees of freedom.

Accepted Answer

The degrees of freedom for a chi-square goodness-of-fit test when testing the goodness-of-fit of a normal distribution with estimated mean and standard deviation for a data with k categories is (k-1). However, since estimating the mean and standard deviation also requires 2 degrees of freedom, the total degrees of freedom for this test becomes (k-3).

Question 5

In a chi-square test of independence the contingency table has 4 rows and 3 columns.The number of degrees of freedom for this test is 6.

Accepted Answer

The degrees of freedom for a chi-square test of independence are calculated as (number of rows - 1) * (number of columns - 1), which in this case is (4 - 1) * (3 - 1) = 3 * 2 = 6.

Question 6

The decision rule in a chi-square goodness-of-fit test is to reject the null hypothesis if the computed chi-square is greater than the table chi-square.

Accepted Answer

This is the correct decision rule for a chi-square goodness-of-fit test. This is correct. In a chi-square goodness-of-fit test, the decision rule is to reject the null hypothesis if the calculated chi-square statistic is greater than the critical value from the chi-square distribution table at the given level of significance and degrees of freedom.

Question 7

A goodness-of-fit test is to be performed to see if consumers prefer any of three package designs (A, B, and C)more than the other two.A sample of 60 consumers is used.What is the expected frequency for category A?

Accepted Answer

Since there are three package designs and the sample size is 60, the expected frequency for each design is 20 (total sample size divided by number of designs). Therefore, the expected frequency for category A is 20.

Question 8

In a chi-square goodness-of-fit test, theoretical frequencies are also called expected frequencies.

Accepted Answer

Theoretical frequencies in a chi-square goodness-of-fit test are calculated based on the expected distribution of values, therefore they are also called expected frequencies. Theoretical frequencies are the frequencies that are expected if the null hypothesis is true, so they are also called expected frequencies in a chi-square goodness-of-fit test.

Question 9

A goodness-of-fit test is to be performed to see if web surfers prefer any of four websites (A, B, C, and D)more than the other three.A sample of 60 consumers is used.What is the expected frequency for website A?

Accepted Answer

Since there are four websites total, we would expect each website to be chosen 1/4 of the time if there is no preference. Therefore, the expected frequency for website A would be:
Expected frequency = (total sample size) x (expected proportion) = 60 x 1/4 = 15. So the best choice is C.

Question 10

A chi-square goodness-of-fit test to determine if the observed frequencies in ten categories are Poisson distributed has nine degrees of freedom.

Accepted Answer

The correct degrees of freedom for a chi-square goodness-of-fit test with ten categories is nine. Thus, the correct answer is B, not A. For a chi-square goodness-of-fit test with k categories and under the assumption of Poisson distribution, the number of degrees of freedom is k-1. Therefore, if there are 10 categories, the degrees of freedom for the test would be 10-1=9.

Question 11

A variable contains five categories.It is expected that data are uniformly distributed across these five categories.To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24.Using $\alpha$ = .01, the observed value of chi-square is ___.

Accepted Answer

The answer of A variable contains five categories.It is expected...

Question 12

A variable contains five categories.It is expected that data are uniformly distributed across these five categories.To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24.Using $\alpha$ = .01, the critical value of chi-square is ___.

Accepted Answer

The answer of A variable contains five categories.It is expected...

Question 13

In a chi-square test of independence the contingency table has 4 rows and 3 columns.The number of degrees of freedom for this test is 7.

Accepted Answer

The number of degrees of freedom for a chi-square test of independence on a contingency table with 4 rows and 3 columns is (4-1) x (3-1) = 6, not 7. The number of degrees of freedom for a chi-square test of independence with a contingency table with 4 rows and 3 columns would be (4-1)*(3-1) = 6. Therefore, the statement is false.

Question 14

The null hypothesis in a chi-square goodness-of-fit test is that the observed distribution is same as the expected distribution.

Accepted Answer

The null hypothesis in a chi-square goodness-of-fit test is that the observed distribution is the same as the expected distribution.

Question 15

The null hypothesis for a chi-square test of independence is that the two variables are not related.

Accepted Answer

The null hypothesis for a chi-square test of independence is that the two variables are not related. The alternative hypothesis is that the two variables are related or dependent. This statement is true. The null hypothesis for a chi-square test of independence states that the two variables being tested are not related or there is no association between them. The alternative hypothesis is that there is a significant association between the two variables.

Question 16

In a chi-square test of independence the contingency table has 4 rows and 3 columns.The number of degrees of freedom for this test is 12.

Accepted Answer

The number of degrees of freedom for a chi-square test of independence with a contingency table of 4 rows and 3 columns is (4-1) x (3-1) = 6.

Question 17

A variable contains five categories.It is expected that data are uniformly distributed across these five categories.To test this, a sample of observed data is gathered on this variable resulting in frequencies of 27, 30, 29, 21, and 24.Using $\alpha$ = .01, the degrees of freedom for this test are ___.

Accepted Answer

The degrees of freedom for a chi-square test for goodness of fit are calculated as the number of categories minus one. Since there are five categories, the degrees of freedom are 5 - 1 = 4.

Question 18

The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated.

Accepted Answer

The answer of The number of degrees of freedom in...

Question 19

In a chi-square goodness-of-fit test, actual frequencies are also called calculated frequencies.

Accepted Answer

Actual frequencies refer to the observed frequencies in the sample, while calculated frequencies are the expected frequencies under the null hypothesis. Actual frequencies refer to the observed values in the data, whereas calculated frequencies are the expected values calculated based on the null hypothesis.

Question 20

A chi-square goodness-of-fit test to determine if the observed frequencies in eight categories are uniformly distributed has seven degrees of freedom.

Accepted Answer

The degrees of freedom for a chi-square goodness-of-fit test with eight categories is the number of categories minus one, which in this case is seven.

Quiz 16: Analysis of Categorical Data