Question 1

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

A chi-square goodness-of-fit test to determine if observed frequencies are Poisson distributed typically has (number of categories - 1) degrees of freedom. In this case, there are ten categories, so there would be nine degrees of freedom, not ten.

Question 2

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.

Question 3

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

Accepted Answer

Theoretical frequencies are indeed referred to as expected frequencies in a chi-square goodness-of-fit test.

Question 4

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 _______.
A)5
B)4
C)3
D)2
E)1

Accepted Answer

To test for uniform distribution, we use the chi-square goodness of fit test. The degrees of freedom for this test are calculated by subtracting 1 from the number of categories. In this case, there are five categories, so the degrees of freedom are 5-1 = 4. Therefore, the answer is (B).

Question 5

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 is the correct formula for calculating degrees of freedom in a chi-square goodness-of-fit test.

Question 6

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 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?
A)1/3
B)20
C)60
D)10
E)30

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 8

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 (number of rows - 1) x (number of columns - 1). In this case, there are 4 rows (age categories) and 3 columns (reading levels), so the expected degrees of freedom would be (4-1) x (3-1) = 6. Therefore, the statement in the prompt that the number of degrees of freedom is 12 is false.

Question 9

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 with k categories is k-1. In this case, there are 7 categories, so the degrees of freedom would be 7-1=6.

Question 10

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 _______.
A)12.09
B)9.82
C)13.28
D)17.81
E)2.09

Accepted Answer

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

Question 11

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

This statement is true. The null hypothesis in a chi-square goodness-of-fit test is that there is no significant difference between the observed distribution and the expected distribution.

Question 12

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?
A)1/4
B)20
C)15
D)10
E)30

Accepted Answer

Since there are four web sites and each one is equally likely to be preferred, the expected frequency for each web site is simply the total sample size (60) divided by the number of web sites (4). Therefore, the expected frequency for web site A is 60/4 = 15. Thus, the correct answer is C) 15.

Question 13

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 _______.
A)7.78
B)15.09
C)9.24
D)13.28
E)15.48

Accepted Answer

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

Question 14

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. If the computed chi-square value is greater than the table chi-square value at the chosen level of significance and degrees of freedom, then the null hypothesis is rejected.

Question 15

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

Accepted Answer

This is because a two-way table is used to display the frequencies of two categorical variables and their relationship to each other, which is also called contingency.

Question 16

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 has (k-1) degrees of freedom, not (k-3) as stated in the statement.

Question 17

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

Accepted Answer

Actual frequencies are the observed frequencies, while calculated frequencies are the expected frequencies based on the null hypothesis.

Question 18

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 19

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)(3-1) = 6, not 7.

Question 20

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...

Quiz 16: Analysis of Categorical Data

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

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

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

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.

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.

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?

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.

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

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 _______.

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

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?

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 _______.

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.

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

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.

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

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

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.

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.

Quiz 16: Analysis of Categorical Data

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

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

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

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.

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.

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?

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.

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

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 α\alphaα = .01,the observed value of chi-square is _______.

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

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?

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 α\alphaα = .01,the critical value of chi-square is _______.

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.

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

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.

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

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

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.

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.

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 _______.

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 _______.