Question 1

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

Accepted Answer

This is correct. The two-way table used for a test of independence is also commonly known as a contingency table.

Question 2

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

Accepted Answer

The degrees of freedom for a chi-square goodness-of-fit test of uniform distribution in seven categories is (7-1) = 6. Therefore, the statement is true.

Question 3

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 4

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

The degrees of freedom for a chi-square goodness-of-fit test are calculated as the number of categories minus the number of parameters estimated minus one, to account for the constraints imposed by the parameters and the total sample size.

Question 5

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

Accepted Answer

A chi-square goodness-of-fit test to determine Poisson distribution with k categories has (k-1) degrees of freedom. Therefore, for ten categories, the degrees of freedom would be (10-1) = 9.

Question 6

A chi-square goodness-of-fit test is being used to test the goodness-of-fit of a uniform distribution for a dataset with "k" categories. This test has (k - 3) degrees of freedom.

Accepted Answer

A chi-square goodness-of-fit test for a uniform distribution with "k" categories has (k-1) degrees of freedom, not (k-3).

Question 7

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

Accepted Answer

The null hypothesis in a chi-square goodness-of-fit test is indeed that the observed distribution is the same as the expected distribution, making answer A true. The alternative hypothesis is that there is a significant difference between the observed and expected distributions.

Question 8

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

In a goodness-of-fit test, the expected frequency for each category is equal. Therefore, the expected frequency for each website is 60/4 = 15. Thus, the best choice is C.

Question 9

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 goodness-of-fit test is k-1, where k is the number of categories. In this case, there are 5 categories, so the degrees of freedom is 5-1 = 4.

Question 10

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

Accepted Answer

Actual frequencies are the observed frequencies in the sample, while calculated frequencies are the frequencies that would be expected under the null hypothesis.

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 critical value of chi-square is ___.

Accepted Answer

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

Question 12

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 13

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 also referred to as expected frequencies.

Question 14

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 with a contingency table of 4 rows and 3 columns is (4-1) x (3-1) = 6, not 7.

Question 15

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...

Question 16

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 there is no association between the two variables being tested. In other words, they are not related. So, statement A is true.

Question 17

When using the chi-square goodness-of-fit test, the type of distribution (uniform, Poisson, normal) being used does not influence the hypothesis test.

Accepted Answer

The type of distribution being tested (uniform, Poisson, normal, etc.) directly influences the expected frequencies calculated for the chi-square goodness-of-fit test, which are crucial for determining how well the observed data fit the expected distribution under the null hypothesis.

Question 18

A researcher is interested in using a chi-square test of independence to determine if age is independent of minutes spent reading. Age is divided into four categories while minutes spent reading is classified as high, medium, low. 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 is calculated as (r-1)*(c-1) where r is the number of categories for one variable and c is the number of categories for the other variable. In this case, there are 4 categories for age and 3 categories for minutes spent reading, so the expected degrees of freedom would be (4-1)*(3-1) = 6. The given value of 12 is incorrect and does not match the expected degrees of freedom. Therefore, the answer is B (False).

Question 19

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, we would expect each design to have an equal frequency of 20 (60/3). Therefore, the expected frequency for category A is 20.

Question 20

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 correct. 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 or equal to the table chi-square at the desired level of significance and degrees of freedom.

Quiz 15: Categorical Versus Categorical: Tests