Question 1

Chi-square analysis of a contingency table provides the answer to the question

Accepted Answer

A)  is there a difference among the categories of a variable? 
B)  is there a difference among the categories of one variable, and also among categories of a second variable? 
C)  is there a relationship between two variables? 
D)  are the categories of one variable the same as those of the other variable? 
A)  is there a difference among the categories of a variable? 
B)  is there a difference among the categories of one variable, and also among categories of a second variable? 
C)  is there a relationship between two variables? 
D)  are the categories of one variable the same as those of the other variable? C

Question 2

The basic element of chi-square is

Accepted Answer

A)    
B)    
C)    
D)   
A)    
B)    
C)    
D)   B

Question 3

In one chi-square problem, each observed frequency was the same as its expected frequency.

Accepted Answer

A)  This would be an unusual even if the null hypothesis were true. 
B)  This would be an unusual even if the null hypothesis were false. 
C)  Chi-square will be zero. 
D)  All of the above are true. 
A)  This would be an unusual even if the null hypothesis were true. 
B)  This would be an unusual even if the null hypothesis were false. 
C)  Chi-square will be zero. 
D)  All of the above are true. D

Question 4

The obtained values of chi-square

Accepted Answer

A)  can be negative if discrepancies have negative values 
B)  can be negative even if no discrepancy is negative 
C)  can be no lower than zero 
D)  cannot be as low as zero 
A)  can be negative if discrepancies have negative values 
B)  can be negative even if no discrepancy is negative 
C)  can be no lower than zero 
D)  cannot be as low as zero

Question 5

For a particular category, we find the difference between expected and observed frequency to differ by 25 points. This will tend to make chi-square large if

Accepted Answer

A)  the difference is positive 
B)  the difference is negative 
C)  fe is small 
D)  fo is small 
A)  the difference is positive 
B)  the difference is negative 
C)  fe is small 
D)  fo is small

Question 6

when

Accepted Answer

A)  both are normally distributed 
B)    
C)    
D)    
A)  both are normally distributed 
B)    
C)    
D)

Question 7

In the chi-square test, a very low (close to 0) value of chi-square implies that

Accepted Answer

A)  the observed frequencies are more like their corresponding expected frequencies than would be expected by chance 
B)  the several observed frequencies are very similar 
C)  the several expected frequencies are very similar 
D)  the positive difference between expected and observed frequencies tend to balance the negative differences 
A)  the observed frequencies are more like their corresponding expected frequencies than would be expected by chance 
B)  the several observed frequencies are very similar 
C)  the several expected frequencies are very similar 
D)  the positive difference between expected and observed frequencies tend to balance the negative differences

Question 8

You wish to see if consumers differ in their preference for three different fast-food restaurants. You conduct a survey with 60 subjects and obtain the following frequencies for preference: restaurant A = 30, restaurant B = 18, and restaurant C = 12. Compute  XS1U1P12S1S1P0
 and perform the test at ($\alpha$ = .05).

Accepted Answer

The answer of You wish to see if consumers differ...

Question 9

For a given level of significance, the critical value of chi-square will be larger

Accepted Answer

A)  when n is larger 
B)  when the number of degrees of freedom is smaller 
C)  when the number of degrees of freedom is larger 
D)  when the number of categories is smaller 
A)  when n is larger 
B)  when the number of degrees of freedom is smaller 
C)  when the number of degrees of freedom is larger 
D)  when the number of categories is smaller

Question 10

In a chi-square goodness-of-fit problem, there are 6 categories, and expected frequencies of 5 in each category. The number of degrees of freedom for this problem is

Accepted Answer

A)  5 
B)  24 
C)  25 
D)  29 
A)  5 
B)  24 
C)  25 
D)  29

Question 11

A random sample of registered voters is selected from each of the three major areas of a western city. Those in the samples are asked for their preferences among three candidates for mayor.   
(a)State (in words) the null hypothesis of independence for this situation in terms of proportions.
(b)Perform the $X^2$ test of independence $(\alpha = .05)$ and draw conclusions.
(c)Do your results from (b) prove that voter preference is unrelated to area of the city? Explain.

Accepted Answer

(a)?The proportions of registered voters

Question 12

We wish to test the null hypothesis that students guess at random on a particular 4-alternative multiple-choice item. The choices for a random sample of 24 students are:
 
 The value of fe for alternative (2) is

Accepted Answer

A)  9 
B)  7 
C)  5 
D)  6 
A)  9 
B)  7 
C)  5 
D)  6

Question 13

Each of a sample of 100 participants at a weekend workshop responds to a particular attitude statement as follows:   
(a) State (in words) the null hypothesis of independence for this situation in terms of proportions.
(b)Compute the expected frequencies under the null hypothesis of independence.
(c)Complete the     XS1U1P12S1S1P0    and draw final conclusions.
(d)Translate each obtained frequency into a proportion based on its row frequency. What interpretation seems likely?

Accepted Answer

(a) The proportions of males holding the

Question 14

Use the following data to answer Questions
  
-The observed frequency for the upper right cell is

Accepted Answer

A)  20 
B)  25 
C)  30 
D)  not determinable from the information given 
A)  20 
B)  25 
C)  30 
D)  not determinable from the information given

Question 15

In a comprehensive review of past real estate sales, researchers noted that even though four styles of homes were offered to potential home buyers with equal frequency, the actual number of purchases of each type of home were slightly different. There were 2,144 homes purchased. Do the observed frequencies indicate any preference for particular styles? Use 
$\alpha$ = .05
(a) Colonial: 514 purchased
(b) Cape Cod: 498 purchased
(c) Victorian: 604 purchased
(d) Salt Box: 528 purchased

Accepted Answer

The answer of In a comprehensive review of past real...

Question 16

Older texts recommended using a "correction for continuity" when  , 
 particularly if fe in one of the categories was less than 5. However, more recent studies have shown that the uncorrected chi-square is reasonably accurate when

Accepted Answer

A)  all fe's are at least 2 
B)  all fe's are at least 3 
C)  the average fe is at least 2 
D)  the average fe is at least 5 
A)  all fe's are at least 2 
B)  all fe's are at least 3 
C)  the average fe is at least 2 
D)  the average fe is at least 5

Question 17

Which, if any, is not a characteristic necessary for obtained values of chi-square to be distributed according to the tabled values of the chi-square distribution?

Accepted Answer

A)  expected frequencies must be equal for all groups 
B)  the null hypothesis must be true 
C)  sampling must be random 
D)  all of the above must be true 
A)  expected frequencies must be equal for all groups 
B)  the null hypothesis must be true 
C)  sampling must be random 
D)  all of the above must be true

Question 18

In the chi-square test, we will reject the null hypothesis if the obtained chi-square is

Accepted Answer

A)  very low 
B)  very high 
C)  either very low or very high 
D)  close to the mean of the tabled distribution of chi-square 
A)  very low 
B)  very high 
C)  either very low or very high 
D)  close to the mean of the tabled distribution of chi-square

Question 19

The contingency table is a form of

Accepted Answer

A)  frequency distribution 
B)  relative frequency distribution 
C)  cumulative frequency distribution 
D)  bivariate frequency distribution 
A)  frequency distribution 
B)  relative frequency distribution 
C)  cumulative frequency distribution 
D)  bivariate frequency distribution

Question 20

Use the following data to answer Questions
  
-The expected frequency for the upper right cell on the hypothesis of independence is

Accepted Answer

A)  20 
B)  25 
C)  30 
D)  not determinable for the information given 
A)  20 
B)  25 
C)  30 
D)  not determinable for the information given

Chi-square analysis of a contingency table provides the answer to the question

The basic element of chi-square is

In one chi-square problem, each observed frequency was the same as its expected frequency.

The obtained values of chi-square

For a particular category, we find the difference between expected and observed frequency to differ by 25 points. This will tend to make chi-square large if

when

In the chi-square test, a very low (close to 0) value of chi-square implies that

For a given level of significance, the critical value of chi-square will be larger

In a chi-square goodness-of-fit problem, there are 6 categories, and expected frequencies of 5 in each category. The number of degrees of freedom for this problem is

We wish to test the null hypothesis that students guess at random on a particular 4-alternative multiple-choice item. The choices for a random sample of 24 students are: The value of f_e for alternative (2) is

Use the following data to answer Questions -The observed frequency for the upper right cell is

Older texts recommended using a "correction for continuity" when , particularly if f_e in one of the categories was less than 5. However, more recent studies have shown that the uncorrected chi-square is reasonably accurate when

Which, if any, is not a characteristic necessary for obtained values of chi-square to be distributed according to the tabled values of the chi-square distribution?

In the chi-square test, we will reject the null hypothesis if the obtained chi-square is

The contingency table is a form of

Use the following data to answer Questions -The expected frequency for the upper right cell on the hypothesis of independence is

Introduction

Frequency Distributions, Percentiles,

Graphic Representation of Frequency Distributions

Central Tendency

Variability and Standard Z Scores

Standard Scores and the Normal Curve

Correlation

Prediction

Interpretive Aspects of Correlation and Regression

Probability

Random Sampling and Sampling Distributions

Introduction to Statistical Inference: Testing Hypotheses About Single Means Z and T

Interpreting the Results of Hypothesis Testing: Effect Size, Type I and Type II Errors, and Power

Testing Hypotheses About the Difference Between Two Independent Groups

Testing for a Difference

Inference About Correlation Coefficients

An Alternative to Hypothesis Testing: Confidence Intervals

Testing for Differences Among Three or More Groups: One-Way Analysis of Variance and Some Alternatives

Factorial Analysis of Variance

Some Almost Assumption-Free Tests

Filters

Exam 20: Chi-Square and Inference About Frequencies

Chi-square analysis of a contingency table provides the answer to the question

The basic element of chi-square is

In one chi-square problem, each observed frequency was the same as its expected frequency.

The obtained values of chi-square

For a particular category, we find the difference between expected and observed frequency to differ by 25 points. This will tend to make chi-square large if

when

In the chi-square test, a very low (close to 0) value of chi-square implies that

For a given level of significance, the critical value of chi-square will be larger

In a chi-square goodness-of-fit problem, there are 6 categories, and expected frequencies of 5 in each category. The number of degrees of freedom for this problem is

We wish to test the null hypothesis that students guess at random on a particular 4-alternative multiple-choice item. The choices for a random sample of 24 students are: The value of fe for alternative (2) is

Use the following data to answer Questions -The observed frequency for the upper right cell is

Older texts recommended using a "correction for continuity" when , particularly if fe in one of the categories was less than 5. However, more recent studies have shown that the uncorrected chi-square is reasonably accurate when

Which, if any, is not a characteristic necessary for obtained values of chi-square to be distributed according to the tabled values of the chi-square distribution?

In the chi-square test, we will reject the null hypothesis if the obtained chi-square is

The contingency table is a form of

Use the following data to answer Questions -The expected frequency for the upper right cell on the hypothesis of independence is

Introduction

Frequency Distributions, Percentiles,

Graphic Representation of Frequency Distributions

Central Tendency

Variability and Standard Z Scores

Standard Scores and the Normal Curve

Correlation

Prediction

Interpretive Aspects of Correlation and Regression

Probability

Random Sampling and Sampling Distributions

Introduction to Statistical Inference: Testing Hypotheses About Single Means Z and T

Interpreting the Results of Hypothesis Testing: Effect Size, Type I and Type II Errors, and Power

Testing Hypotheses About the Difference Between Two Independent Groups

Testing for a Difference

Inference About Correlation Coefficients

An Alternative to Hypothesis Testing: Confidence Intervals

Testing for Differences Among Three or More Groups: One-Way Analysis of Variance and Some Alternatives

Factorial Analysis of Variance

Some Almost Assumption-Free Tests

Filters

We wish to test the null hypothesis that students guess at random on a particular 4-alternative multiple-choice item. The choices for a random sample of 24 students are: The value of f_e for alternative (2) is

Older texts recommended using a "correction for continuity" when , particularly if f_e in one of the categories was less than 5. However, more recent studies have shown that the uncorrected chi-square is reasonably accurate when