Question 1

A cafeteria proposes to serve 4 main entrees. For planning purposes, the manager expects that the proportions of each that will be selected by his customers will be:  Of the first 100 customers, 44 selected chicken, 24 selected roast beef, 13 select steak, and 10 selected fish. Should the manager revise his estimates? Use  = 0.01.  = ______________
Critical Value(s) = ______________
Conclusion: ______________
The manager ______________ revise his estimates.

Accepted Answer

The answer of A cafeteria proposes to serve 4 main...

Question 2

A contingency table classifies data with respect to two qualitative variables that are each divided into two or more categories.

Accepted Answer

A) True 
 B)False

Question 3

A study of the purchase decisions of three stock portfolio managers, A, B, C, was conducted to compare the numbers of stock purchases that resulted in profits over a time period less than or equal to 1 year. One hundred randomly selected purchases were examined for each of the managers.  Do the data provide evidence of differences among the rates of successful purchases for the three managers?
Compute  = ______________
The p-value is ______________.
Conclude that there ______________ enough information to conclude that the proportion of successful purchases will differ among the managers.

Accepted Answer

The answer of A study of the purchase decisions of...

Question 4

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

Accepted Answer

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.

Question 5

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 17.894. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that 0.05 < p-value < 0.10.

Accepted Answer

A) True 
 B)False

Question 6

The personnel manager of a consumer products company asked a random sample of employees how they felt about the work they were doing. The following table gives a breakdown of their responses by age.  Is there sufficient evidence to conclude that the level of job satisfaction is related to age? Use  = 0.10.
What is  ?
______________
Critical Value = ______________
Conclusion: ______________
Job satisfaction ______________ related to age.

Accepted Answer

The answer of The personnel manager of a consumer products...

Question 7

The degrees of freedom associated with a chi-square test of independence where data are summarized in a contingency table with r rows and c columns equal the number of rows times the number of columns in the table; that is, rc.

Accepted Answer

A) True 
 B)False

Question 8

The degrees of freedom associated with a goodness-of-fit test equal the number of rows times the number of columns in the table.

Accepted Answer

A) True 
 B)False

Question 9

The area to the right of a chi-square value is 0.05. For 9 degrees of freedom, the table value is:

Accepted Answer

A)  16.9190 
B)  3.32511 
C)  4.16816 
D)  19.0228 
E)  21.1

Question 10

For a chi-square distributed random variable with 10 degrees of freedom and a level of significance of 0.025, the chi-square table value is 20.4831. The computed value of the test statistics is 16.857. This will lead us to reject the null hypothesis.

Accepted Answer

A) True 
 B)False

Question 11

In a chi-square test of independence with 6 degrees of freedom and a level of significance of 0.05, the critical value from the chi-square table is 12.5916. The computed value of the test statistics is 11.264. This will lead us to reject the null hypothesis.

Accepted Answer

A) True 
 B)False

Question 12

Because the chi-square random variable is a sum of squares, it cannot take on negative values.

Accepted Answer

A) True 
 B)False

Question 13

Suppose you wish to test the null hypothesis that three binomial parameters  ,  , and  are equal versus the alternative hypothesis that at least two of the parameters differ. Independent random samples of 100 observations were selected from each of the populations. The data are shown in the table:  Write the null and alternative hypotheses for testing the equality of the three binomial proportions.  :  ______________
Test statistic:  = ______________
What is the p-value?
______________
______________  .
There is ______________ sufficient evidence to indicate that the proportions depend upon the population from which they were drawn.

Accepted Answer

The answer of Suppose you wish to test the null...

Question 14

If we want to perform a two-tail test for differences between two populations of nominal data with exactly two categories, we can employ either the z-test of  , or the chi-square test of homogeneity, since squaring the value of the z statistic yields the value of  statistics.

Accepted Answer

A) True 
 B)False

Question 15

A librarian knows from old records that the percentages of checked-out materials which are fiction, nonfiction, children's books, books on tape, and magazines are 35%, 25%, 20%, 10%, and 10%, respectively. The material checked out in each of the categories in a recent survey of 600 randomly chosen library items is listed below.  Use these data to assess whether there has been a change in the distribution of checked-out library materials. State the hypotheses to be tested and use  = 0.01 to interpret your results.
The hypotheses are:  :  = _______,  = _______,  = _______,  = _______,  = _______  :
______________ from the specified value(s).
Compute  :
______________
Thus we ______________  .
Conclude that ______________ from those specified in  .

Accepted Answer

The answer of A librarian knows from old records that...

Question 16

If we want to conduct a two-tail test of a population proportion, we can employ:

Accepted Answer

A)  z-test of a population proportion 
B)  the chi-square goodness-of-fit test since 
C)  the chi-square test of independence 
D)  z-test of a population proportion and the chi-square goodness-of-fit test since 
E)  z-test of a population proportion and the chi-square test of independence

Question 17

Five brands of orange juice are displayed side by side in several supermarkets in the city of Chicago. It was noted that in one day, 180 customers purchased orange juice. Of these, 30 picked Brand A, 40 picked Brand B, 25 picked Brand C, 35 picked Brand D, and 50 picked brand E. In Chicago, can you conclude at the 5% significance level that there is a preferred brand of orange juice?
Compute  :
______________
Reject  when  > ______________.
Conclude that there ______________ preferred brand of orange juice in Chicago.

Accepted Answer

The answer of Five brands of orange juice are displayed...

Question 18

A sample survey of 850 people in Chicago was conducted in 2001 to see how people get to work. The results are shown in the frequency table below.  A study of the same nature was conducted in 1990 and revealed 12% walk, 67% drive an automobile, 18% take a bus, and 3% ride a bicycle.
Do the current data support that the proportions are the same as in 1990? Use  .
Compute  :
______________
One should ______________  .
Conclude that the current data ______________ that the proportions in 2001 are the same as in 1990.

Accepted Answer

The answer of A sample survey of 850 people in...

Question 19

The number of Americans who visit fast-food restaurants regularly has grown steadily over the last decade. For this reason, marketing experts are interested in the demographics of fast-food customers. Is a customer's preference for a fast- food chain affected by the age of the customer? If so, advertising might need to target a particular age group. Suppose a random sample of 400 fast-food customers aged 16 and older was selected, and their favorite fast-food restaurants along with their age groups were recorded, as shown in the table:  Use an appropriate method to determine whether or not a customer's fast-food preference is dependent on age.
Compute  :
______________
What is the p-value?
______________
Conclude that there ______________ a dependence between age group and favorite fast food restaurant.
Write a short paragraph presenting your statistical conclusions and their practical implications for marketing experts.
________________________________________________________

Accepted Answer

The answer of The number of Americans who visit fast-food...

Question 20

The chi-square technique has numerous applications, including:

Accepted Answer

A)  testing the alleged independence of two qualitative variables 
B)  making inferences about the relative sizes of more than two population proportions 
C)  conducting a goodness-of-fit-test to determine whether data are consistent with data drawn from a particular probability distribution 
D)  all of these 
E)  none of these

Exam 14: Analysis of Categorical Data

A contingency table classifies data with respect to two qualitative variables that are each divided into two or more categories.

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

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 17.894. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that 0.05 < p-value < 0.10.

The degrees of freedom associated with a chi-square test of independence where data are summarized in a contingency table with r rows and c columns equal the number of rows times the number of columns in the table; that is, rc.

The degrees of freedom associated with a goodness-of-fit test equal the number of rows times the number of columns in the table.

The area to the right of a chi-square value is 0.05. For 9 degrees of freedom, the table value is:

For a chi-square distributed random variable with 10 degrees of freedom and a level of significance of 0.025, the chi-square table value is 20.4831. The computed value of the test statistics is 16.857. This will lead us to reject the null hypothesis.

In a chi-square test of independence with 6 degrees of freedom and a level of significance of 0.05, the critical value from the chi-square table is 12.5916. The computed value of the test statistics is 11.264. This will lead us to reject the null hypothesis.

Because the chi-square random variable is a sum of squares, it cannot take on negative values.

If we want to perform a two-tail test for differences between two populations of nominal data with exactly two categories, we can employ either the z-test of , or the chi-square test of homogeneity, since squaring the value of the z statistic yields the value of statistics.

If we want to conduct a two-tail test of a population proportion, we can employ:

The chi-square technique has numerous applications, including: