Question 1

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

Accepted Answer

In a chi-square goodness-of-fit test, actual frequencies refer to the observed frequencies, while calculated frequencies refer to the expected frequencies under the null hypothesis.

Question 2

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 3

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

E

Question 4

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 5

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 6

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 no preference is assumed, the expected frequency for each category is the total sample size divided by the number of categories. Therefore, for 60 consumers divided among 3 categories (A, B, and C), the expected frequency for each is 60/3 = 20.

Question 7

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

In a chi-square goodness-of-fit test, the degrees of freedom are calculated as the number of categories minus one. Therefore, for seven categories, the degrees of freedom would be 7 - 1 = 6.

Question 8

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

Accepted Answer

In a chi-square goodness-of-fit test, if the computed chi-square value is greater than the critical value from the chi-square distribution table (at a given significance level), the decision rule is to reject the null hypothesis, indicating that the observed frequencies significantly differ from the expected frequencies.

Question 9

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

Accepted Answer

The null hypothesis in a chi-square test of independence states that there is no association between the two categorical variables, meaning they are independent of each other.

Question 10

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 rows and c is the number of columns in the contingency table. Here, with age divided into four categories (r = 4) and minutes spent reading divided into three categories (c = 3), the degrees of freedom would be (4 - 1) * (3 - 1) = 3 * 2 = 6.

Question 11

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

Accepted Answer

The expected frequency for each Web site is calculated by dividing the total number of consumers (60) by the number of Web sites (4), which equals 15.

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 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 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 degrees of freedom for a chi-square test of independence are calculated as (number of rows - 1) * (number of columns - 1), so for a 4x3 table, it would be (4-1)*(3-1) = 3*2 = 6.

Question 14

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

Accepted Answer

A contingency table, also known as a cross-tabulation or crosstab, is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. It is commonly used in statistics to analyze the relationship between two categorical variables, hence its use in tests of independence.

Question 15

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 indeed states that there is no significant difference between the observed and expected frequencies in the categories being analyzed, implying the distributions are the same.

Question 16

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 17

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 18

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 19

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 answer of A chi-square goodness-of-fit test to determine if...

Question 20

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

Accepted Answer

In a chi-square goodness-of-fit test, the theoretical frequencies refer to the expected frequencies calculated under the null hypothesis, indicating how often each category is expected to occur according to the model being tested.

Quiz 16: Analysis of Categorical Data