Question 1

Consider a cell in a contingency table. Given the cell's row total of 200, the cell's column total of 75, and a sample size of 1,000, the cell's expected frequency:
A) equals 10
B) equals 15
C) equals 20
D) equals 25
E) cannot possibly be determined without additional information

Accepted Answer

The answer of Consider a cell in a contingency table....

Question 2

In a chi-square test of independence, the value of the test statistic was  = 9.572, and the critical value at  was 11.1433. Thus,
A) we fail to reject the null hypothesis at
B) we reject the null hypothesis at
C) we don't have enough evidence to accept or reject the null hypothesis at
D) we should decrease the level of significance in order to reject the null hypothesis
E) none of these

Accepted Answer

The test statistic (9.572) is less than the critical value (11.1433), so we fail to reject the null hypothesis at the given level of significance.

Question 3

The number of degrees of freedom for a contingency table with 6 rows and 6 columns is:
A) 36
B) 25
C) 12
D) 6
E) 0

Accepted Answer

The degrees of freedom for a contingency table are calculated as (number of rows - 1) * (number of columns - 1). For a 6x6 table, this is (6-1)*(6-1) = 5*5 = 25.

Question 4

A market research study was conducted to compare three different brands of car oil. The results of the study are summarized below.  Use the accompanying MINITAB output and  = 0.005 to determine whether the brand of oil is independent of opinion.
Compute  = ______________
Reject  when  > ______________.
Conclude that the two variables are ______________.

Accepted Answer

The answer of A market research study was conducted to...

Question 5

The president of a state university collected data from students concerning building a new library, and classified the responses into different categories (strongly agree, agree, undecided, disagree, strongly disagree) and according to whether the student was male or female. To determine whether the data provide sufficient evidence to indicate that the responses depend upon gender, the most appropriate test is:
A) chi-square goodness-of-fit test
B) chi-square test of a contingency table (test of independence)
C) chi-square test of normality
D) none of these
E) all of these

Accepted Answer

The most appropriate test to determine whether the responses depend upon gender is the chi-square test of a contingency table, also known as the test of independence. This test compares the observed frequency of each category for males and females to the expected frequency if there was no relationship between gender and response. The chi-square goodness-of-fit test would only be appropriate if the data were collected from one group and compared to expected frequencies based on a specific distribution. The chi-square test of normality would only be appropriate if the data were being tested for normality. None of these tests are appropriate for testing whether the data provide evidence that the responses depend upon gender, except for the chi-square test of a contingency table. Therefore, the answer is only B.

Question 6

A chi-square test of a contingency table with 4 rows and 5 columns shows that the value of the test statistic is 22.18. The most accurate statement that can be made about the p-value for this test is that:
A) p-value is greater than 0.05
B) p-value is smaller than 0.025
C) p-value is greater than 0.025 but smaller than 0.05
D) p-value is greater than 0.10
E) Not enough information is given to determine the p- value.

Accepted Answer

Since we have 4 rows and 5 columns, the degrees of freedom for this test would be (4-1) x (5-1) = 12.
Using a chi-square distribution table or calculator with 12 degrees of freedom, we can find that the critical value for a 0.05 level of significance is 21.03 and the critical value for a 0.025 level of significance is 24.72.
Since the calculated chi-square value of 22.18 falls between these two critical values, we can conclude that the p-value for this test is greater than 0.025 but smaller than 0.05. Therefore, the most accurate statement about the p-value is C: "p-value is greater than 0.025 but smaller than 0.05."

Question 7

Which statistical technique is appropriate when we wish to analyze the relationship between two qualitative variables with two or more categories?
A) The chi-square test of a multinomial experiment.
B) The chi-square test of a contingency table.
C) The t-test of the difference between two means.
D) The z test of the difference between two proportions.
E) None of these.

Accepted Answer

The chi-square test of a contingency table is appropriate when we wish to analyze the relationship between two qualitative variables with two or more categories. This test is used to determine if there is a significant association between the variables, and if so, what the nature of that association is.

Question 8

A contingency table:
A) classifies data with respect to two qualitative variables
B) divides each variable into two or more categories
C) contains numbers that show the frequency of occurrence of all possible combinations of categories
D) all of these
E) none of these

Accepted Answer

A contingency table organizes data by classifying it with respect to two qualitative variables, dividing each variable into two or more categories, and displaying the frequency of occurrence of all possible combinations of categories. Therefore, all of these options are correct.

Question 9

Contingency tables are used in:
A) testing independence of two samples
B) testing dependence in matched pairs
C) testing independence of two populations
D) describing a single population
E) testing independence of two quantitative variables in a population

Accepted Answer

Contingency tables are used to test the independence of two populations. They can be used to find the relationship between two categorical variables from two different populations.

Question 10

A pollster was interested in determining whether three television dramas are equally preferable among men and women. The following data was recorded:  Compute  = ______________
Reject  when  > ______________.
Conclude that the preference of television drama is ______________ the viewer's gender.

Accepted Answer

The answer of A pollster was interested in determining whether...

Question 11

A chi-square test of independence is applied to a contingency table with 4 rows and 5 columns for two qualitative variables. The degrees of freedom for this test will be:
A) 20
B) 16
C) 15
D) 12
E) 9

Accepted Answer

The degrees of freedom for a chi-square test of independence is calculated as (number of rows - 1) * (number of columns - 1). For a table with 4 rows and 5 columns, this is (4-1)*(5-1) = 3*4 = 12.

Question 12

A chi-square test of independence with 10 degrees of freedom results in a test statistic of 19.25. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that:
A) p-value < 0.025
B) 0.025 < p-value < 0.05
C) 0.05 < p-value < 0.10
D) 0.10 < p-value < 0.20
E) p-value > 0.2

Accepted Answer

The answer of A chi-square test of independence with 10...

Question 13

The owner of Fit Forever Health Club is considering adding an indoor swimming pool to his facility. The manager decided to take a survey to determine whether member opinion about the addition of a pool was independent of the age of the member. Two hundred members were selected at random and asked to state their opinion. The following data was recorded:  What is  ?
______________
What is the p-value associated with the test?
______________
Conclude that member's opinion concerning the addition of an indoor pool is ______________ the member's age.

Accepted Answer

The answer of The owner of Fit Forever Health Club...

Question 14

Which of the following statements about a goodness-of-fit test is false?
A) It determines the likelihood that sample data have been generated from a population that conforms to a specified type of probability distribution.
B) It compares the entire shapes of two (discrete or continuous) probability distributions: one describing known population data and the other one describing hypothetical sample data.
C) The aim of the test might be limited to identifying only the family to which the underlying distribution belongs.
D) The aim of the test might be limited to identifying only the family to which the underlying distribution belongs or it might go further, seeking even to identify a particular member of that family.
E) None of these.

Accepted Answer

A goodness-of-fit test is used to compare a population distribution to a sample to see if they match. However, it does not compare two probability distributions, but rather it compares the observed distribution of the sample to the expected distribution under the null hypothesis. The null hypothesis is that the sample was drawn from a population with a specific distribution. Therefore, statement B is false.

Question 15

Which of the following statements about the chi-square distribution is false?
A) A different chi-square distribution exists for each possible number of degrees of freedom.
B) Because the chi-square random variable is a sum of squared deviations, negative values are impossible.
C) All values range between zero and one.
D) All chi-square distributions are skewed to the right.
E) All of these.

Accepted Answer

The statement "All values range between zero and one" is false. The range of values for a chi-square distribution is actually from 0 to infinity.

Question 16

The chi-square test of independence is based upon:
A) two qualitative variables
B) two quantitative variables
C) three or more qualitative variables
D) three or more quantitative variables
E) a quantitative and a qualitative variable

Accepted Answer

The chi-square test of independence is used to analyze the association between two categorical variables. Therefore, the best choice is A, which indicates two qualitative variables.

Question 17

Which of the following statements about a contingency table test is false?
A) The nature of the sampling distribution of chi-square depends on the number of degrees of freedom associated with the problem under investigation.
B) The degrees of freedom are found as (r - 2)(c - 2), where r represents number of rows and c represents number of columns.
C) The contingency table must have a minimum of 2 rows and 2 columns.
D) All of these.
E) None of these.

Accepted Answer

The degrees of freedom for a contingency table are calculated as (r - 1)(c - 1), where r is the number of rows and c is the number of columns, not as (r - 2)(c - 2) as stated in option B.

Question 18

A contingency table test with 4 rows and 30 degrees of freedom implies that the table must have:
A) 7 columns
B) 9 columns
C) 11 columns
D) 13 columns
E) 15 columns

Accepted Answer

The degrees of freedom for a contingency table are calculated as (rows - 1) * (columns - 1). Given 4 rows and 30 degrees of freedom, solving the equation (4-1) * (columns - 1) = 30 gives columns - 1 = 10, so the table must have 11 columns.

Question 19

The chi-square test of a contingency table is based upon:
A) two qualitative variables
B) two quantitative variables
C) three or more qualitative variables
D) three or more quantitative variables
E) all of these

Accepted Answer

The chi-square test of a contingency table is based on two qualitative variables. It is used to test the independence between two categorical variables. Therefore, the best choice is A).

Question 20

A contingency table test with 4 rows and 15 degrees of freedom implies:
A) 5 columns
B) 6 columns
C) 9 columns
D) 11 columns
E) 60 columns

Accepted Answer

For a contingency table test, the number of columns is equal to the number of categories being compared in both the row and column variables. Degrees of freedom (df) are calculated by (number of rows - 1) x (number of columns - 1). Therefore, (df + 1) = number of cells in the table. Solving this equation for the number of columns, we get: number of columns = (df + 1) / number of rows - 1. Plugging in the values given in the question, we get: number of columns = (15 + 1) / 4 - 1 = 3.5. Since the number of columns has to be a whole number, the closest option is 6, making B the correct answer.

Quiz 14: Analysis of Categorical Data

Consider a cell in a contingency table. Given the cell's row total of 200, the cell's column total of 75, and a sample size of 1,000, the cell's expected frequency:

In a chi-square test of independence, the value of the test statistic was = 9.572, and the critical value at was 11.1433. Thus,

The number of degrees of freedom for a contingency table with 6 rows and 6 columns is:

A chi-square test of a contingency table with 4 rows and 5 columns shows that the value of the test statistic is 22.18. The most accurate statement that can be made about the p-value for this test is that:

Which statistical technique is appropriate when we wish to analyze the relationship between two qualitative variables with two or more categories?

A contingency table:

Contingency tables are used in:

A pollster was interested in determining whether three television dramas are equally preferable among men and women. The following data was recorded: Compute = Reject when > . Conclude that the preference of television drama is __ the viewer's gender.

A chi-square test of independence is applied to a contingency table with 4 rows and 5 columns for two qualitative variables. The degrees of freedom for this test will be:

A chi-square test of independence with 10 degrees of freedom results in a test statistic of 19.25. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that:

Which of the following statements about a goodness-of-fit test is false?

Which of the following statements about the chi-square distribution is false?

The chi-square test of independence is based upon:

Which of the following statements about a contingency table test is false?

A contingency table test with 4 rows and 30 degrees of freedom implies that the table must have:

The chi-square test of a contingency table is based upon:

A contingency table test with 4 rows and 15 degrees of freedom implies: