Deck 15: Chi-Square Applications

Question 1

Tests of hypotheses for nominal or ordinal levels of measurement are called nonparametric or distribution-free tests.

Answer 1

True

Question 2

A goodness-of-fit test is a nonparametric test involving a set of observed frequencies and a corresponding set of expected frequencies.

Answer 2

True

Question 3

In a goodness-of-fit test,the sum of the expected frequencies need not equal the sum of the observed frequencies.

Answer 3

False

Question 4

If there are more than two cells,chi-square should not be applied if more than 50 percent of the expected frequency cells have expected frequencies of less than ten.

Question 5

Nonparametric tests require no assumptions about the shape of the population distribution.

Question 6

The chi-square test statistic used in a goodness-of-fit test has k-1 degrees of freedom.

Question 7

The chi-square goodness-of-fit test can be applied if there are equal or unequal expected frequencies.

Question 8

The chi-square goodness-of-fit test is appropriate for nominal and ordinal levels of data.

Question 9

Nonparametric tests of hypotheses,also called distribution free tests,require the population to be normally distributed.

Question 10

For a goodness-of-fit test,the following are possible null and alternate hypotheses:
H₀: Sales are uniformly distributed among the five locations.
H₁: Sales are not uniformly distributed among the five locations.

Question 11

The shape of the chi-square distribution depends on the size of the sample.

Question 12

In chi-square applications,the sum of the differences between expected and observed frequencies must equal zero.

Question 13

The chi-square distribution is positively skewed.

Question 14

The claim that "male and female students at Coastal Carolina University prefer different parking lots on campus" is an example of a chi-square null hypothesis.

Question 15

In the goodness-of-fit test,the chi-square distribution is used to determine how well an observed distribution of observations "fits" an expected distribution of observations.

Question 16

A small number of cells with expected frequencies less than 5,might result in an erroneous conclusion for the application of the chi-square distribution.

Question 17

In a goodness-of-fit test,the sum of the expected frequencies must equal the sum of the observed frequencies.

Question 18

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.

Question 19

For a goodness-of-fit test,the number of degrees of freedom is k-2,where k is the number of categories.

Question 20

For the goodness-of-fit test,the use of the chi-square statistic would be permissible in the following problem.

Question 21

The educational level and the social activity of a sample of executives follow. What does the expected frequency for the "above average" social activity and "high school" education equal?

A)9.50
B)60.00
C)22.50
D)28.50

Question 22

For a contingency table,the expected frequency for a cell is found by dividing the row total by the grand total.

Question 23

The chi-square distribution is

A)positively skewed.
B)negatively skewed.
C)normally distributed.
D)negatively or positively skewed.

Question 24

When conducting a hypothesis test with chi-square analysis,the rejection region in a chi-square distribution is always in the upper or right tail.

Question 25

The shape of the chi-square distribution changes for each number of degrees of freedom.

Question 26

Which of the following assumptions is necessary to apply a nonparametric test of hypothesis using the chi-square distribution?

A)Normal population is required
B)Interval scale of measurement is required
C)Population variance must be known
D)Both "a" and "c"
E)None of these

Question 27

The chi-square distribution can assume

A)only positive values.
B)only negative values.
C)negative and positive values or zero.
D)only zero.

Question 28

When conducting a hypothesis test with chi-square analysis,the rejection region is in the lower or left tail of a chi-square distribution.

Question 29

A question has these possible choices-excellent,very good,good,fair and unsatisfactory.How many degrees of freedom are there using the goodness-of-fit test to the sample results?

A)0
B)2
C)4
D)5

Question 30

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?

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 31

What is our decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 9.488 and the computed value is 6.079?

A)The difference is probably due to sampling error;do not reject the null hypothesis
B)Not due to chance;reject the null hypothesis
C)Not due to chance;do not reject the alternate hypothesis
D)Too close;reserve judgment

Question 32

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?

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

Question 33

Two chi-square distributions were plotted on the same chart.One distribution was for 3 degrees of freedom and the other was for 12 degrees of freedom.Which distribution would tend to approach a normal distribution?

A)3 degrees
B)12 degrees
C)15 degrees
D)All would

Question 34

When conducting a hypothesis test with chi-square analysis,the null hypothesis is rejected when the differences between the expected and observed frequencies are relatively large.

Question 35

Which of the following are correct statements regarding the chi-square distribution?

A)Distribution is negatively skewed
B)Chi-square is based on two sets of degrees of freedom,one for the numerator and one for the denominator
C)Its shape is based on the degrees of freedom
D)All of these are true
E)None of these are true

Question 36

If the computed value of a chi-square statistic is less than the critical chi-square value,reject the null hypothesis at a predetermined Type I error rate.

Question 37

A distributor of personal computers has five locations in the city.The sales in units for the first quarter of the year were as follows: What is the critical value at the 0.01 level of risk?

A)7.779
B)15.033
C)13.277
D)5.412

Question 38

What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories?

A)3.841
B)5.991
C)7.815
D)11.070

Question 39

The following table classifies an individual in two ways-by gender and by educational choice. What is this two-way classification called?

A)Goodness-of-fit test
B)Frequency table
C)ANOVA table
D)Contingency table

Question 40

To analyze data cross-classified in a contingency table,how are the degrees of freedom found?

A)N - 1
B)Rows - Columns
C)(Rows)* (Columns)
D)(Rows - 1)* (Columns - 1)

Question 41

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

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

Question 42

The computed chi-square value is positive because the difference between the observed and expected frequencies is

A)squared.
B)linear.
C)uniform.
D)always positive.

Question 43

For any chi-square goodness-of-fit problem,the number of degrees of freedom is found by

A)n - k - 1.
B)k - 1.
C)n + 1.
D)n + k.

Question 44

When determining how well an observed set of frequencies fit an expected set of frequencies the test is a

A)F test.
B)t test.
C) test.
D)test for association.

Question 45

A 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: How many degrees of freedom are there?

A)0
B)3
C)4
D)5

Question 46

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. How many degrees of freedom are there?

A)2
B)3
C)4
D)5

Question 47

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?

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

Question 48

Which of the following can be used to test the hypothesis that two nominal variables are related?

A)a contingency table.
B)a chi-square table.
C)an ANOVA table.
D)a scatter diagram.

Question 49

A sample of 100 production workers is obtained.The workers are classified by gender (male,female)and by age (under 20,20-29,30-39 and 40 or over).How many degrees of freedom are there?

A)0
B)3
C)6
D)5

Question 50

A 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 kind of frequencies are the numbers 12,9,11,10,and 9 called?

A)Acceptance
B)Critical value
C)Expected
D)Observed

Question 51

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 expected frequency for people who are undecided about the project and have property front-footage between 45 and 120 feet?

A)2.2
B)3.9
C)5.0
D)7.7

Question 52

The chi-square has

A)one distribution.
B)two distributions.
C)a family of distributions.
D)a uniform distribution.

Question 53

Which of the following are correct statements regarding the goodness-of-fit test?

A)Data may be of nominal scale
B)Population must be normal
C)All the expected frequencies must be equal
D)All of these are true
E)None of these are true

Question 54

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 expected frequency for people who are in favor of the project and have less than 45 feet of property foot-frontage?

A)10
B)12
C)35
D)50

Question 55

A 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 expected frequency?

A)9
B)10
C)11
D)12

Question 56

For a chi-square test involving a contingency table,suppose the null hypothesis is rejected.We conclude that the two variables are

A)linear.
B)curvilinear.
C)not related.
D)related.

Question 57

The chi-square distribution becomes more symmetrical as

A)number of variables increase.
B)the chi-square value increases.
C)degrees of freedom decrease.
D)degrees of freedom increase.

Question 58

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 expected frequency for people against the project and who have over 120 feet of property foot-frontage?

A)1.1
B)3.9
C)5.0
D)5.5

Question 59

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 5% level of significance?

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

Question 60

In a goodness-of-fit test,the null hypothesis (no difference between sets of observed and expected frequencies)is rejected when the

A)computed chi-square is less than the critical value.
B)difference between the observed and expected frequencies is significantly large.
C)difference between the observed and expected frequencies is small.
D)difference between the observed and expected frequencies occurs by chance.

Question 61

What does the chi-square distribution approach with large degrees of freedom? _________________________

Question 62

A recent study of the relationship between social activity and education showed the following results. Using 0.05 as the significance level,what is the critical value for the test statistic?

A)9.488
B)5.991
C)7.815
D)3.841

Question 63

A recent study of the relationship between social activity and education showed the following results. The appropriate test to analyze the relationship between social activity and education is:

A)Regression analysis
B)Analysis of variance
C)Contingency table analysis
D)Goodness-of-fit

Question 64

A recent study of the relationship between social activity and education showed the following results. The degrees of freedom for the analysis is:

A)1
B)2
C)3
D)4

Question 65

What should the expected frequencies be for a goodness-of-fit test if there are only two cells? ___________

Question 66

A recent study of the relationship between social activity and education showed the following results. What is the value of the test statistic?

A)100
B)135.24
C)50
D)4.94

Question 67

A recent study of the relationship between social activity and education showed the following results. Based on the analysis,what can be concluded?

A)Social activity and education are correlated.
B)Social activity and education are not related.
C)Social activity and education are related.
D)No conclusion is possible.

Question 68

The computed value of chi-square statistic is always positive because the difference between the observed frequencies and the expected frequencies is ______________.

Question 69

Recently,students in a marketing research class were interested in the driving behavior of students.Specifically,the marketing students were interested if exceeding the speed limit was related to social activity.They collected the following responses from 100 randomly selected students: Using 0.05 as the significance level,what is the critical value for the test statistic?

A)9.488
B)5.991
C)7.815
D)3.841

Question 70

A 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?

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

Question 71

Recently,students in a marketing research class were interested in the driving behavior of students.Specifically,the marketing students were interested if exceeding the speed limit was related to social activity.They collected the following responses from 100 randomly selected students: What is the value of the test statistic?

A)83.67
B)9.89
C)50
D)4.94

Question 72

Recently,students in a marketing research class were interested in the driving behavior of students.Specifically,the marketing students were interested if exceeding the speed limit was related to social activity.They collected the following responses from 100 randomly selected students: The null hypothesis for the analysis is:

A)There is no relationship between gender and driving behavior.
B)The correlation between driving behavior and gender is zero.
C)As driving behavior increases,gender increases.
D)The mean of driving behavior equals the mean of gender.

Question 73

What statistical test is used to determine how well an observed set of data fits an expected set of data? ________________________________

Question 74

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 kind of table is this classification? __________________

Question 75

A 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 critical value of chi-square with $\alpha$ = 0.05?

A)11.070
B)12.592
C)13.388
D)15.033

Question 76

A recent study of the relationship between social activity and education showed the following results. The appropriate test statistic for the analysis is a:

A)F-statistic
B)T-statistic
C)Chi-square statistic
D)Z-statistic

Question 77

A recent study of the relationship between social activity and education showed the following results. The null hypothesis for the analysis is:

A)There is no relationship between social activity and education.
B)The correlation between social activity and education is zero.
C)As social activity increases,education increases.
D)The mean of social activity equals the mean of education.

Question 78

Recently,students in a marketing research class were interested in the driving behavior of students.Specifically,the marketing students were interested if exceeding the speed limit was related to social activity.They collected the following responses from 100 randomly selected students: Based on the analysis,what can be concluded?

A)Driving behavior and gender are correlated.
B)Driving behavior and gender are not related.
C)Driving behavior and gender are related.
D)No conclusion is possible.

Question 79

Recently,students in a marketing research class were interested in the driving behavior of students.Specifically,the marketing students were interested if exceeding the speed limit was related to social activity.They collected the following responses from 100 randomly selected students: The degrees of freedom for the analysis is:

A)1
B)2
C)3
D)4

Question 80

When sampling from a population,small differences between observed and expected frequencies may be due to _____________.