Question 1

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

Accepted Answer

Theoretical frequencies are expected frequencies in a chi-square goodness-of-fit test.

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 12.

Accepted Answer

The number of degrees of freedom for a chi-square test of independence is calculated using the formula (r-1)(c-1), where r is the number of rows and c is the number of columns in the contingency table. Therefore, in this case, the number of degrees of freedom would be (4-1)(3-1) = 6, not 12.

Question 3

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 the degrees of freedom in a chi-square goodness-of-fit test.

Question 4

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 is that none of the expected frequencies should be less than 5, not 30.

Question 5

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 chi-square goodness-of-fit test for a normal distribution with k categories has (k-2) degrees of freedom, not (k-3).

Question 6

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 for Poisson distribution has k-1 degrees of freedom, where k is the number of categories. In this case, there are 10 categories, so there should be 9 degrees of freedom (10-1=9).

Question 7

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 whether the observed data is uniformly distributed, we use the Chi-Square Goodness of Fit test. The degrees of freedom for this test is calculated as (number of categories - 1). In this case, there are 5 categories, so the degrees of freedom is 5-1 = 4. Therefore, the answer is B.

Question 8

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 9

Use the chi-square test of independence to perform contingency analysis.

Accepted Answer

The answer of Use the chi-square test of independence to...

Question 10

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 are calculated by subtracting 1 from the number of categories. Therefore, in this case, 7 - 1 = 6 degrees of freedom.

Question 11

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.

Question 12

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 13

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, the two variables are independent of each other. Therefore, if there is evidence to reject the null hypothesis, it suggests that there is a relationship between the variables being tested.

Question 14

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 15

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. These are two distinct concepts in a chi-square goodness-of-fit test.

Question 16

Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.

Accepted Answer

The answer of Use the chi-square goodness-of-fit test to analyze...

Question 17

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

Accepted Answer

This is true. A two-way table used for a test of independence is often referred to as a contingency table because it shows the contingency, or dependence, between two categorical variables.

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

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

Accepted Answer

Since there are four websites, the expected frequency for each website is 1/4 of the total sample size. 
Expected frequency for website A = 1/4 * 60 = 15. Therefore, the best choice is C.

Question 20

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 with 4 rows and 3 columns is (4-1) x (3-1) = 6.

Quiz 16: Analysis of Categorical Data

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

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.

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.

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

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.

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

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.

Use the chi-square test of independence to perform contingency analysis.

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

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.

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

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

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?

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

Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.

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

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 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?

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.

Quiz 16: Analysis of Categorical Data

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

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.

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.

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

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.

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

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.

Use the chi-square test of independence to perform contingency analysis.

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

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.

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

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

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?

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

Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension.

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

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 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?

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.

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 ___.