Question 1

How many degrees of freedom do we use for the chi square goodness of fit test?

Accepted Answer

A)  k, where k represents the number of classes/categories. 
B)  k - 1, where k represents the number of classes/categories. 
C)  k - 1, where k represents the number of data values. 
D)  k, where k represents the number of data values. 
A)  k, where k represents the number of classes/categories. 
B)  k - 1, where k represents the number of classes/categories. 
C)  k - 1, where k represents the number of data values. 
D)  k, where k represents the number of data values.

Question 2

Three new colors have been proposed for the Jeep Grand Cherokee vehicle. They are silvered-blue, almond, and willow green. The null hypothesis for a goodness-of-fit test would be

Accepted Answer

A)  willow green preferred over the other colours. 
B)  no preference between the colours. 
C)  any one color preferred over the other colours. 
D)  impossible to determine. 
A)  willow green preferred over the other colours. 
B)  no preference between the colours. 
C)  any one color preferred over the other colours. 
D)  impossible to determine.

Question 3

A student asked a statistics professor if grades were marked "on the curve." The professor decided to give the student a project to determine if last year's statistics grades were normally distributed. The professor told the student that last year's mean mark was 70 with a standard deviation of 10 and to use the following results.     Using the data from this Mega stat printout, you determine:

Accepted Answer

A)  the letter grades are evenly distributed when tested at the 0.05 level of significance. 
B)  the letter grades are not normally distributed when tested at the 0.01 level of significance. 
C)  the letter grades are normally distributed when tested at the 0.05 level of significance. 
D)  the letter grades are not normally distributed when tested at the 0.05 level of significance. 
E)  the letter grades are not normally distributed when tested at either the 0.01 or 0.05 level of significance. 
A)  the letter grades are evenly distributed when tested at the 0.05 level of significance. 
B)  the letter grades are not normally distributed when tested at the 0.01 level of significance. 
C)  the letter grades are normally distributed when tested at the 0.05 level of significance. 
D)  the letter grades are not normally distributed when tested at the 0.05 level of significance. 
E)  the letter grades are not normally distributed when tested at either the 0.01 or 0.05 level of significance.

Question 4

i. The minimum computed value of chi-square is one. ii. The chi-square distribution is a positively skewed distribution.
iii. The lowest level of data for which the chi-square goodness-of-fit test is appropriate is the nominal level.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 5

At a recent automobile show, a sample of 125 people produced the following results. Use the 0.05 significance level to determine if there is a relationship between age and model preferred.   Based on the analysis above, what can be concluded?

Accepted Answer

A)  Buyer's age and car model preference are not related. 
B)  Buyer's age and car model preference are related. 
C)  The mean of age is the same as the mean of car model preference. 
D)  No conclusion can be made. 
A)  Buyer's age and car model preference are not related. 
B)  Buyer's age and car model preference are related. 
C)  The mean of age is the same as the mean of car model preference. 
D)  No conclusion can be made.

Question 6

i. For a goodness-of-fit test, the following are possible null and alternate hypotheses. Null: Sales are uniformly distributed among the five locations. Alternate: Sales are not uniformly distributed among the five locations. ii. In the goodness-of-fit test, the chi-square distribution is used to determine how well an observed set of observations "fits" an "expected" set of observations.
iii. The sum of the expected frequencies and the sum of the observed frequencies must be equal.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 7

What is our decision for a goodness-of-fit test with a computed value of chi-square of 1.273 and a critical value of 13.388?

Accepted Answer

A)  Do not reject the null hypothesis. 
B)  Reject the null hypothesis. 
C)  Unable to reject or not reject the null hypothesis based on data. 
D)  Should take a larger sample. 
A)  Do not reject the null hypothesis. 
B)  Reject the null hypothesis. 
C)  Unable to reject or not reject the null hypothesis based on data. 
D)  Should take a larger sample.

Question 8

i. The claim that "male and female University of Toledo students prefer different parking lots on campus" is an example of a chi-square null hypothesis. ii. For contingency table analysis using the chi-square test, multiplying the number of rows minus 1 by the number of columns minus 1 will give you the degrees of freedom.
iii. For a contingency table, the expected frequency for a cell is found by dividing the row total by the grand total.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (ii) is a correct statement but not (i) or (iii). 
C)  (iii) is a correct statement but not (i) or (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (ii) is a correct statement but not (i) or (iii). 
C)  (iii) is a correct statement but not (i) or (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 9

i. The shape of the chi-square distribution depends on the size of the sample. ii. Small differences between observed and expected frequencies are due to chance.
iii. The chi-square distribution with large degrees of freedom approaches a normal distribution.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 10

At a recent car show, a sample of 125 people produced the following results. Use the 0.01 significance level to determine if there is a relationship between age and model preferred.

Accepted Answer

A)  Reject the null hypothesis, there is a significant relationship between age and model preferred at the 1% level of significance. 
B)  Unable to reject the null hypothesis, there is a significant relationship between age and model preferred at the 1% level of significance. 
C)  Reject the null hypothesis, there is insufficient evidence to show a significant relationship between age and model preference at the 1% level of significance. 
D)  Unable to reject the null hypothesis, there is insufficient evidence to show a significant relationship between age and model preference at the 1% level of significance. 
A)  Reject the null hypothesis, there is a significant relationship between age and model preferred at the 1% level of significance. 
B)  Unable to reject the null hypothesis, there is a significant relationship between age and model preferred at the 1% level of significance. 
C)  Reject the null hypothesis, there is insufficient evidence to show a significant relationship between age and model preference at the 1% level of significance. 
D)  Unable to reject the null hypothesis, there is insufficient evidence to show a significant relationship between age and model preference at the 1% level of significance.

Question 11

Canadian Accounting classifies accounts receivable as "current", "late", and "not collectible". Industry figures show that 60% of A/R are current, 30% are late, and 10% are uncollectible. A law firm in Markham Ontario has 500 accounts receivable: 320 are current, 100 are late and 80 are not collectible. Are these numbers in agreement with the industry distribution?   Using the data from this Mega stat printout, you determine:

Accepted Answer

A)  the Markham firm's data reflect the national average, when tested at the 0.10 level of significance. 
B)  the Markham firm's data reflect the national average, when tested at the 0.05 level of significance. 
C)  the Markham firm's data reflect the national average, when tested at the 0.01 level of significance. 
D)  the Markham firm's data do not reflect the national average, when tested above a 0.01 level of significance. 
A)  the Markham firm's data reflect the national average, when tested at the 0.10 level of significance. 
B)  the Markham firm's data reflect the national average, when tested at the 0.05 level of significance. 
C)  the Markham firm's data reflect the national average, when tested at the 0.01 level of significance. 
D)  the Markham firm's data do not reflect the national average, when tested above a 0.01 level of significance.

Question 12

The personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:   What is the calculated value of chi-square?

Accepted Answer

A)  1.0 
B)  0.5 
C)  0.8 
D)  8.0 
A)  1.0 
B)  0.5 
C)  0.8 
D)  8.0

Question 13

i. The claim that "male and female University of Toledo students prefer different parking lots on campus" is an example of a chi-square null hypothesis. ii. For a contingency table, the expected frequency for a cell is found by dividing the row total by the grand total.
iii. For contingency table analysis using the chi-square test, multiplying the number of rows minus 1 by the number of columns minus 1 will give you the degrees of freedom.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are false statements only (iii) is correct. 
C)  (ii) is a correct statement but not (i) or (iii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are false statements only (iii) is correct. 
C)  (ii) is a correct statement but not (i) or (iii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 14

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance of front footage. A randomly selected sample of 100 property owners was contacted and the results are shown below.   What is the critical value at the 10% level of significance?

Accepted Answer

A)  7.779 
B)  9.236 
C)  9.488 
D)  11.070 
A)  7.779 
B)  9.236 
C)  9.488 
D)  11.070

Question 15

i. Nonparametric tests require no assumptions about the shape of the population distribution. ii. There is not one, but a family of chi-square distributions. There is a chi-square distribution for 1 degree of freedom, another for 2 degrees of freedom, another for 3 degrees of freedom, and so on.
iii. The chi-square distribution with large degrees of freedom approaches a normal distribution.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 16

At a recent automobile show, a sample of 125 people produced the following results. Use the 0.01 significance level to determine if there is a relationship between age and model preferred.   Based on the analysis above, what can be concluded?

Accepted Answer

A)  Buyer's age and car model preference are not related. 
B)  Buyer's age and car model preference are related. 
C)  The mean of age is the same as the mean of car model preference. 
D)  No conclusion can be made. 
A)  Buyer's age and car model preference are not related. 
B)  Buyer's age and car model preference are related. 
C)  The mean of age is the same as the mean of car model preference. 
D)  No conclusion can be made.

Question 17

The following table shows the adjustment to civilian life and place of residence.   What is the critical value for this contingency table at the 0.01 level of significance?

Accepted Answer

A)  9.488 
B)  2.070 
C)  11.345 
D)  13.277 
A)  9.488 
B)  2.070 
C)  11.345 
D)  13.277

Question 18

i. There is not one, but a family of chi-square distributions. There is a chi-square distribution for 1 degree of freedom, another for 2 degrees of freedom, another for 3 degrees of freedom, and so on. ii. The shape of the chi-square distribution depends on the size of the sample.
iii. Small differences between observed and expected frequencies are due to chance.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 19

Which of the following is not a characteristic of the chi square distribution?

Accepted Answer

A)  Its shape is based on the sample size. 
B)  It is not negative. 
C)  It is positively skewed. 
D)  It approaches a normal distribution as the degrees of freedom increase. 
A)  Its shape is based on the sample size. 
B)  It is not negative. 
C)  It is positively skewed. 
D)  It approaches a normal distribution as the degrees of freedom increase.

Question 20

Canadian Accounting classifies accounts receivable as "current", "late", and "not collectible". Industry figures show that 60% of A/R are current, 30% are late, and 10% are uncollectible. A law firm in Markham Ontario has 500 accounts receivable: 310 are current, 125 are late and 65 are not collectible. Are these numbers in agreement with the industry distribution?   Using the data from this Mega stat printout, you determine:

Accepted Answer

A)  the Markham firm's data reflect the national average, when tested at the 0.10 level of significance. 
B)  the Markham firm's data reflect the national average, when tested at the 0.05 level of significance. 
C)  the Markham firm's data reflect the national average, when tested at the 0.01 level of significance. 
D)  the Markham firm's data do not reflect the national average, when tested above a 0.01 level of significance. 
A)  the Markham firm's data reflect the national average, when tested at the 0.10 level of significance. 
B)  the Markham firm's data reflect the national average, when tested at the 0.05 level of significance. 
C)  the Markham firm's data reflect the national average, when tested at the 0.01 level of significance. 
D)  the Markham firm's data do not reflect the national average, when tested above a 0.01 level of significance.

How many degrees of freedom do we use for the chi square goodness of fit test?

Three new colors have been proposed for the Jeep Grand Cherokee vehicle. They are silvered-blue, almond, and willow green. The null hypothesis for a goodness-of-fit test would be

i. The minimum computed value of chi-square is one. ii. The chi-square distribution is a positively skewed distribution. iii. The lowest level of data for which the chi-square goodness-of-fit test is appropriate is the nominal level.

At a recent automobile show, a sample of 125 people produced the following results. Use the 0.05 significance level to determine if there is a relationship between age and model preferred. Based on the analysis above, what can be concluded?

What is our decision for a goodness-of-fit test with a computed value of chi-square of 1.273 and a critical value of 13.388?

i. The shape of the chi-square distribution depends on the size of the sample. ii. Small differences between observed and expected frequencies are due to chance. iii. The chi-square distribution with large degrees of freedom approaches a normal distribution.

At a recent car show, a sample of 125 people produced the following results. Use the 0.01 significance level to determine if there is a relationship between age and model preferred.

At a recent automobile show, a sample of 125 people produced the following results. Use the 0.01 significance level to determine if there is a relationship between age and model preferred. Based on the analysis above, what can be concluded?

The following table shows the adjustment to civilian life and place of residence. What is the critical value for this contingency table at the 0.01 level of significance?

Which of the following is not a characteristic of the chi square distribution?

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

One-Sample Tests of Hypothesis

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters

Exam 14: Chi-Square Applications

How many degrees of freedom do we use for the chi square goodness of fit test?

Three new colors have been proposed for the Jeep Grand Cherokee vehicle. They are silvered-blue, almond, and willow green. The null hypothesis for a goodness-of-fit test would be

i. The minimum computed value of chi-square is one. ii. The chi-square distribution is a positively skewed distribution. iii. The lowest level of data for which the chi-square goodness-of-fit test is appropriate is the nominal level.

At a recent automobile show, a sample of 125 people produced the following results. Use the 0.05 significance level to determine if there is a relationship between age and model preferred. Based on the analysis above, what can be concluded?

What is our decision for a goodness-of-fit test with a computed value of chi-square of 1.273 and a critical value of 13.388?

i. The shape of the chi-square distribution depends on the size of the sample. ii. Small differences between observed and expected frequencies are due to chance. iii. The chi-square distribution with large degrees of freedom approaches a normal distribution.

At a recent car show, a sample of 125 people produced the following results. Use the 0.01 significance level to determine if there is a relationship between age and model preferred.

At a recent automobile show, a sample of 125 people produced the following results. Use the 0.01 significance level to determine if there is a relationship between age and model preferred. Based on the analysis above, what can be concluded?

The following table shows the adjustment to civilian life and place of residence. What is the critical value for this contingency table at the 0.01 level of significance?

Which of the following is not a characteristic of the chi square distribution?

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

One-Sample Tests of Hypothesis

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters