Deck 15: Nonparametric Methods: Nominal Level Hypothesis Tests

Question 1

A question has these possible responses: excellent,very good,good,fair,and unsatisfactory. What are the degrees of freedom for a goodness-of-fit test to test the hypothesis that responses are uniformly distributed?

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

Answer 1

4

Question 2

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

Answer 2

False

Question 3

A t-statistic is useful for computing an expected normal distribution.

Answer 3

False

Question 4

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 5

To test the null hypothesis that a set of sample data is normally distributed,we compare an expected normal distribution of the data to an observed distribution of the data.

Question 6

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

Question 7

If we are testing the difference between two population proportions,it is assumed that the two populations are approximately normal and have equal variances.

Question 8

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 9

The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.

Question 10

The shape of the chi-square distribution depends on the number of degrees of freedom.

Question 11

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

Question 12

In testing the difference between two population proportions,we pool the two sample proportions to estimate the population proportion.

Question 13

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 14

The chi-square distribution is positively skewed.

Question 15

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

Question 16

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 17

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 18

Some important uses of the chi-square include testing for the association of two categorical variables.

Question 19

The variance of the chi-square distribution is equal to one.

Question 20

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

Question 21

The chi-square distribution is ________.

A)positively skewed
B)negatively skewed
C)normally distributed
D)uniformly distributed

Question 22

The contingency table for a sample of corporate executives classified by educational level and social activity follows. 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 23

A distributor of personal computers has five locations in a city. In the year's first quarter,the sales in units were: For a goodness-of-fit test that sales were the same for all locations,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 24

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 25

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

A)Fail to reject the null hypothesis; the difference is probably due to sampling error.
B)Reject the null hypothesis.
C)Fail to reject the alternate hypothesis.
D)It is too close; reserve judgment.

Question 26

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

A)A contingency table analysis
B)A goodness-of-fit
C)ANOVA table
D)A regression analysis

Question 27

The following table classifies 100 individuals using two variables,gender and college attended. What is this two-way classification called?

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

Question 28

Three new colors have been proposed for the Jeep Grand Cherokee vehicle. They are silver 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)there is no preference between the colors
C)any one color is preferred over the other colors
D)it is impossible to determine

Question 29

Which of the following assumptions is necessary to apply a goodness-of-fit test?

A)The population must be normally distributed.
B)The data are measured with a nominal or ordinal scale.
C)The population variance must be known.
D)The population mean must be known.

Question 30

What are the degrees of freedom for a contingency table analysis?

A)n - 1
B)Rows − Columns
C)(Rows)× (Columns)
D)(Rows − 1)× (Columns − 1)

Question 31

For people released from prison,the following table shows their 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 32

The chi-square statistic has ________.

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

Question 33

The chi-square statistic ________.

A)is greater than or equal to zero
B)is less than or equal to zero
C)can be any value
D)is equal to zero

Question 34

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

A)Variables are based on the nominal measurement scale.
B)Population must be normal.
C)All the expected frequencies must be equal.
D)All the expected frequencies must be unequal.

Question 35

The chi-square distribution becomes more symmetrical as the ________.

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

Question 36

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 37

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

A)Do not reject the null hypothesis.
B)Reject the null hypothesis.
C)We are unable to reject or not reject the null hypothesis based on data.
D)We should take a larger sample.

Question 38

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

A)n - k − 1
B)k − 1
C)n + 1
D)n + k

Question 39

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

A)The 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)The shape of the distribution is based on the degrees of freedom.
D)The variance of the distribution is equal to one.

Question 40

Which chi-square distribution would be closest to a normal distribution?

A)The distribution with 3 degrees of freedom
B)The distribution with 12 degrees of freedom
C)The distribution with 15 degrees of freedom
D)The distribution with 9 degrees of freedom

Question 41

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The degrees of freedom for the analysis are ________.

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

Question 42

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The appropriate test statistic for the analysis is a(n)________.

A)F-statistic
B)t-statistic
C)chi-square statistic
D)z-statistic

Question 43

A recent study of the relationship between social activity and education for a sample of corporate executives 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 44

A recent study of the relationship between social activity and education for a sample of corporate executives 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 45

Recently,students in a marketing research class were interested in the driving behavior of students. Specifically,the marketing students were interested in finding out 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 46

A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis 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 47

Recently,students in a marketing research class were interested in the driving behavior of students. Specifically,the marketing students were interested in finding out 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)9.890
C)50
D)4.94

Question 48

Recently,students in a marketing research class were interested in the driving behavior of students. Specifically,the marketing students were interested in finding out 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 49

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The appropriate test to analyze the relationship between social activity and education is ________.

A)a regression analysis
B)an analysis of variance
C)a contingency table analysis
D)a goodness-of-fit test

Question 50

A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis 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 51

A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. Use the 0.01 level of significance. The sample results are:: How many degrees of freedom are there?

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

Question 52

When determining how well an observed set of frequencies fits an expected set of frequencies,what is the test statistic?

A)F-statistic
B)t-statistic
C)X^2-statistic
D)z-statistic

Question 53

Recently,students in a marketing research class were interested in the driving behavior of students. Specifically,the marketing students were interested in finding out if exceeding the speed limit was related to gender. 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 speeding
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 54

Recently,students in a marketing research class were interested in the driving behavior of students. Specifically,the marketing students were interested in finding out 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 are ________.

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

Question 55

A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis 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 a chi-square with α = 0.05?

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

Question 56

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 57

A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. What is the value of the chi-square test statistic?

A)100
B)83.67
C)50
D)4.94

Question 58

A recent study of the relationship between social activity and education for a sample of corporate executives 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 59

A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis 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 12,9,11,10,9,and 9 called?

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

Question 60

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 61

To test if an observed frequency distribution with five classes is normally distributed,we need to find ________.

A)the t-statistic
B)the expected,normally distributed class frequencies
C)the class marks
D)the class relative frequencies

Question 62

A frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. Based on the normal distribution,what is the probability that an observation would be in this class?

A)0.4938
B)0.4772
C)0.0166
D)−0.0166

Question 63

Suppose we test H₀: π₁ = π₂ at the 0.05 level of significance. If the z-test statistic is −1.07,what is our decision?

A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
C)Take a larger sample.
D)Reserve judgment.

Question 64

A frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. What are the standard normal z-statistics for the class limits?

A)−20 and 20
B)−2.5 and −2.0
C)2.0 and 2.5
D)−50 and −40

Question 65

A survey of property owners' opinions about a street-widening project was taken to determine if owners' opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown next. 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 66

A sample of 250 adults tried the new multigrain cereal Wow! A total of 187 rated it as excellent. In a sample of 100 children,66 rated it as excellent. Using the 0.1 significance level,the researcher wishes to show that adults like the cereal better than children. What is the pooled proportion?

A)0.723
B)1.408
C)0.494
D)0.807

Question 67

A survey of property owners' opinions about a street-widening project was taken to determine if owners' opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown next. What is the critical value at the 10% level of significance?

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

Question 68

A survey of property owners' opinions about a street-widening project was taken to determine if owners' opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown next. What is the critical value at the 5% level of significance?

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

Question 69

A frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. Based on the normal distribution,what is the probability that an observation would be in this class?

A)0.1359
B)0.3413
C)0.4772
D)0.8185

Question 70

To test if an observed frequency distribution with five classes is normally distributed,we compute probabilities for each class based on a(n)________.

A)standard normal distribution
B)chi-square distribution
C)student's t-distribution
D)F-distribution

Question 71

A survey of property owners' opinions about a street-widening project was taken to determine if owners' opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown next. How many degrees of freedom are there?

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

Question 72

A survey of property owners' opinions about a street-widening project was taken to determine if owners' opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown next. 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 73

How is a pooled estimate of the population proportion represented?

A)p_c
B)z
C)π
D)nπ

Question 74

A sample of 250 adults tried the new multigrain cereal Wow! A total of 187 rated it as excellent. In a sample of 100 children,66 rated it as excellent. Using the 0.1 significance level,the researcher wishes to show that adults like the cereal better than children. Which of the following is the alternate hypothesis?

A)H₁: πA = πC
B)H₁: πA < πC
C)H₁: πA > πC
D)H₁: πA ≠ πC

Question 75

A frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. What are the standard normal z-statistics for the class limits?

A)−20 and 20
B)−2.0 and −1.0
C)200 and 220
D)1.0 and 2.0

Question 76

A survey of property owners' opinions about a street-widening project was taken to determine if owners' opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown next. 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 77

To test if an observed frequency distribution with five classes is normally distributed,we need to ________.

A)compute an F-statistic
B)calculate a t-statistic
C)convert the class marks to standard normal z-statistics
D)convert the class limits to standard normal z-statistics

Question 78

In a market test of a new chocolate raspberry coffee,a poll of 400 people from Dobbs Ferry showed 250 preferred the new coffee. In Irvington,170 out of 350 people preferred the new coffee. To test the hypothesis that there is no difference in preferences between the two villages,what is the null hypothesis?

A)H₀: π₁ < π₂
B)H₀: π₁ > π₂
C)H₀: π₁ = π₂
D)H₀: π₁ ≠ π₂

Question 79

If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance,what are the alternative hypothesis and rejection region?

A)H₁: π₁ ≠ π₂; z > +1.645 and z < −1.645
B)H₁: π₁ ≠ π₂; z > +1.960 and z < −1.960
C)H₁: π₁ > π₂; z < −1.645
D)H₁: π₁ > π₂; z < −1.960

Question 80

In a market test of a new chocolate raspberry coffee,a poll of 400 people (sample 1)from Dobbs Ferry showed 250 preferred the new coffee. In Irvington,170 out of 350 people (sample 2)preferred the new coffee. To test the hypothesis that a higher proportion of people in Dobbs Ferry prefer the new coffee,what is the alternate hypothesis?

A)H₁: π₁ < π₂
B)H₁: π₁ > π₂
C)H₁: π₁ = π₂
D)H₁: π₁ ≠ π₂