Statistics A Tool for Social Research International Edition 9th Edition by Joseph F. Healey – Test Bank

Statistics A Tool for Social Research International Edition 9th Edition by Joseph F. Healey – Test Bank

Chapter 11

HYPOTHESIS TESTING IV

Chi square

Multiple Choice Questions

• The popularity of the Chi Square test is largely due to

1. easy computations
2. the fact that it can be computed only for interval-ratio level variables
3. the need to assume a normal sampling distribution
4. the relative ease with which the model assumptions can be satisfied

Answer: d Page: 272 LO: 3

• The chi square test is frequently used because it is relatively easy to satisfy the model assumptions (step 1 of the five-step model). These assumptions require, in the case of chi square,

1. a normal population distribution
2. no assumption about the shape of the sampling distribution
3. expected frequencies of equal value
4. a difference in expected and observed frequencies

Answer: b Page: 272 LO: 3

• Which assumption about level of measurement is made for the Chi square test?

1. all variables are at least ordinal in level of measurement
2. all variables are at least interval-ratio in level of measurement
3. all variables are nominal in level of measurement
4. at least one variable must be ordinal in level of measurement

Answer: c Page: 272 LO: 3

• Chi square is one of a class of statistics called

1. nonparametric
2. parametric
3. semi-parametric
4. parametrically symmetrical

Answer: a Page: 272 LO: 3

• Unlike other tests of significance, Chi square easily handles situations in which

1. the variables of interest have more than two categories or scores
2. the variables of interest have less than two categories or scores
3. variables are all ordinal in level of measurement
4. degrees of freedom exceed 100

Answer: a Page: 272 LO: 3

• To conduct a chi square test, the variables must first be organized into a

1. univariate table
2. bivariate table
3. list, which is then ranked
4. frequency distributions

Answer: b Page: 273 LO: 2

• Unlike other tests of significance, chi square is based on

1. a bivariate table
2. means as well as proportions
3. continuous variables only
4. ordinal-level variables only

Answer: a Page: 273 LO: 2

• A bivariate table in which both variables have three categories has

1. three cells
2. six cells
3. nine cells
4. thirty-three cells

Answer: c Page: 273 LO: 2

• A bivariate table in which one variable had three categories and the other variable had four categories would have

1. four cells
2. six cells
3. nine cells
4. twelve cells

Answer: d Page: 273 LO: 2

• In the context of chi square, variables are independent if

1. they are related
2. cause and effect can be proved
3. the obtained chi square falls in the critical region
4. the score of a case on one variable has no effect on the score of the case on the

other variable

Answer: d Page: 274 LO: 3

• Which pattern of cell frequencies in a 2×2 table would indicate that the variables are independent?

1. all cell frequencies are exactly the same
2. there are a different number of cases in each of the four cells
3. only the cells in the top row of the table have cases in them
4. there are no cases in any cell

Answer: a Page: 274 LO: 3

• In a 2×2 table, all cell frequencies are exactly the same. This is consistent with which of the following conditions?

1. the variables are both continuous
2. the sample is a cluster sample
3. the variables are independent
4. the variables are dependent

Answer: c Page: 274 LO: 3

• If two variables are independent, the cell frequencies will be

1. exactly the same
2. concentrated in only two of the cells
3. less than the expected frequencies
4. determined by random chance

Answer: d Page: 274 LO: 4

• In the chi square test of hypothesis, the null hypothesis states that the variables are

1. dependent
2. independent
3. causally related
4. non-random

Answer: b Page: 274 LO: 4

• The Chi square test is based on the assumption that

1. the variables are dependent
2. the expected frequencies are not produced by random chance
3. samples are non-random
4. the null hypothesis is true

Answer: d Page: 274 LO: 4

• When the null hypothesis in the chi square test for independence is true, there should be

1. large difference between the observed frequencies and the expected frequencies
2. little difference between the observed frequencies and the expected frequencies
3. no difference between the observed frequencies and the marginals
4. no difference between the row and the column marginals

Answer: b Page: 274 LO: 4

• Cell frequencies computed under the assumption that the null hypothesis is true are called

1. observed frequencies
2. experimental frequencies
3. expected frequencies
4. random frequencies

Answer: c Page: 274 LO: 4

• In the Chi square test, expected frequencies are computed by

1. adding the observed frequency to N and subtracting the number of cells
2. multiplying the observed frequencies by the row marginals and dividing by degrees of freedom
3. multiplying the proper row and column marginals for each cell and dividing by N
4. adding the proper row and column marginals together and dividing by N

Answer: c Page: 275 LO: 4

• If the row and column marginals of the expected frequencies are not equal to those of the observed frequencies

1. an arithmetic error has occurred
2. Yate’s correction must be applied
3. the null hypothesis must be rejected
4. switch to the ANOVA test

Answer: a Page: 276 LO: 4

• The row and column marginals for the expected frequencies are always ________ those of the observed frequencies.

1. greater than
2. the same as
3. less than
4. different from

Answer: b Page: 276 LO: 4

• If Chi square obtained has a negative value

1. an arithmetic error has been made
2. a one-tailed test is called for
3. the row and column variables must be switched
4. the null hypothesis must be rejected

Answer: a Page: 277 LO: 4

• The value of the chi square test statistic is always

1. zero or a positive number
2. greater than the number of cells in the bivariate table
3. equal to or greater than the critical value
4. greater than the degrees of freedom

Answer: a Page: 277 LO: 4

• A researcher reports that her obtained chi square of -17.56 is significant because it exceeds the critical Chi square of -3.841 for an alpha of .05 with 2 degrees of freedom. What mistake has been made?

1. neither critical nor obtained Chi squares can have negative values
2. it is impossible to have only 2 degrees of freedom
3. it is impossible for obtained Chi square to exceed 10
4. a one-tailed test should have been used

Answer: a Page: 277 LO: 4

• The sampling distribution for chi squares is

1. shaped like any other normal curve
2. not normally distributed
3. bimodal
4. all of the above

Answer: b Page: 278 LO: 4

• In the Chi square test for independence, the research hypothesis is

1. always one-tailed
2. the variables are dependent
3. the variables are independent
4. expected frequencies are greater than observed frequencies

Answer: b Page: 278 LO: 4

• In the Chi square test for independence, the null hypothesis and the research hypothesis

1. always contradict each other
2. always agree with each other
3. are never actually stated
4. are usually both rejected

Answer: a Page: 278 LO: 4

• In the Chi square test, degrees of freedom are

1. N – 1
2. N₁ + N₂ – 2
3. (r + 1)(c + 1)
4. (r – 1)(c – 1)

Answer: d Page: 278 LO: 4

• How many degrees of freedom does a 3 x 3 bivariate table have?

1. 8
2. 6
3. 4
4. 3

Answer: c Page: 278 LO: 4

• In a 2×2 table, if one cell frequency is known,

1. all other cell frequencies are determined
2. two other cell frequencies are determined
3. one other cell frequency is determined
4. none of the other cell frequencies is determined

Answer: a Page: 279 LO: 4

• In a research study conducted to determine if arrests were related to the socioeconomic class of the offender, the chi square critical score was 9.488 and the chi square test statistic was 12.2. We can conclude that

1. the variables are independent
2. being in a certain socioeconomic class causes arrests
3. the variables are dependent
4. the probability of getting these results by random chance alone is 0.5.

Answer: c Page: 279 LO: 1 and 4

• An obtained chi square of 10.78 has been calculated. Critical Chi square is 3.841. What should be concluded?

1. nothing — information is incomplete
2. reject the null hypothesis, the variables are not independent
3. reject the null hypothesis, the variables are independent
4. fail to reject the null hypothesis

Answer: b Page: 279 LO: 4

• Chi square has been used to test the relationship between gender and support for abortion. The null hypothesis has been rejected. What may be concluded?

1. support for abortion depends on gender
2. gender and support for abortion are not related
3. females are more supportive of abortion
4. males are more supportive of abortion

Answer: a Page: 279 LO:1 and 4

• A Chi square test has been conducted to assess the relationship between marital status and church attendance. The obtained Chi square is 23.45 and the critical Chi square is 9.488. What may be concluded?

1. reject the null hypothesis, church attendance and marital status are dependent
2. reject the null hypothesis, church attendance and marital status are independent
3. fail to reject the null hypothesis, church attendance and marital status are dependent
4. fail to reject the null hypothesis, church attendance and marital status are independent

Answer: a Page: 279 LO: 1 and 4

• In order to identify the pattern of the relationship in a bivariate table, we need to compute

1. row percentages
2. column percentages
3. total percentages
4. row proportions

Answer: b Page: 281 LO: 4

• According to the text, there is a “gender gap” in American politics and

1. women are more likely to vote for the Democratic candidate
2. women are more likely to vote
3. men are more likely to vote
4. men are more likely to vote for the Democratic candidate

Answer: a Page: 282 LO: 4

• According to the text, in the 2008 presidential election, women were more likely to vote for

1. McCain
2. Bush
3. Kerry
4. Obama

Answer: d Page: 282 LO: 4

• The chi square goodness-of-fit test can be used when

1. degrees of freedom are less than one
2. column percentages are equal
3. sample size is very large
4. the distribution of a single variable must be tested for significance

Answer: d Page: 284 LO: 4

• For the chi square goodness-of-fit test, the null hypothesis would be that

1. the variables are independent
2. the variables are dependent
3. the distribution of the variable is determined by random chance
4. the distribution of the variable is not determined by random chance

Answer: c Page: 285 LO: 4

• Unlike the chi square test of independence, in the chi square goodness of fit test, the expected frequencies are

1. not used
2. computed
3. determined from the null hypothesis
4. the same as the observed frequencies

Answer: c Page: 285 LO: 4

• Some potential difficulties arise in the chi square test when

1. sample size is small
2. sample size is very large
3. many cells have expected frequencies of five or less
4. all of the above

Answer: d Page: 287 LO: 5

• For Chi square, a small sample is one in which

1. many expected frequencies are less than 5
2. many observed frequencies are less than 5
3. N is less than 100
4. N is less than 50

Answer: a Page: 285 LO: 5

• When cell frequencies are small and 2 x 2 tables are used in the chi square test, an adjustment to the value of chi square can be made by applying

1. Yate’s correction for continuity
2. a different value to the expected frequencies
3. a different value to the observed frequencies
4. any of the above

Answer: a Page: 285 LO: 5

• Yate’s correction for small sample size

1. reduces the value of the difference between f_o and f_e by .5 before squaring
2. increases the value of the difference between f_o and f_e by .5 before squaring
3. reduces the degrees of freedom by one half
4. increases the degrees of freedom by one half

Answer: a Page: 285 LO: 5

• A problem with large samples in the chi square test is that the test statistic

1. increases at the same rate as sample size and trivial relationships may seem important
2. decreases as sample size increases and may cause Type I errors
3. fluctuates so much that the results are completely unreliable
4. is always elevated above the neutral area

Answer: a Page: 288 LO: 5

• A researcher reports a ² (obtained) of 75.34 ( =.05, df = 1, ² (critical) = 3.84, N = 13,678). The researcher claims that the relationship is extremely significant. What issue should be raised?

1. degrees of freedom are much too small for a sample this large.
2. alpha is too low
3. sample size is very large and the actual relationship between the variables might be trivial
4. the value for ² (critical) is much too low

Answer: c Page: 288 LO: 5

• For the chi square test using very large samples, there may be a difference between

1. randomness and independence
2. expected and calculated frequencies
3. statistical significance and importance
4. dependent variables and dependent relationships

Answer: c Page: 288 LO: 5

• Chi square is used to test relationships for their

1. empirical importance
2. logical importance
3. statistical significance
4. theoretical importance

Answer: c Page: 288 LO: 5

• One limitation of the Chi square test (and all tests of hypothesis) is that they cannot tell us if relationships between variables are

1. significant
2. random
3. by chance
4. important

Answer: d Page: 288 LO: 5

• A test of the relationship between social class and socialization values was reported in the text. Which of the following was a result of this test?

1. there is a significant relationship between “think for self” and social class
2. there was no relationship between socialization values and social class
3. people from all social classes strongly endorsed obedience as an essential goal of socialization
4. only people from the highest social classes gave any support at all to independent thinking as an important socialization goal

Answer: a Page: 289-290 LO: 1 and 4

• According to the theory presented in the text, which social class should have the strongest support for obedience as a goal of socialization?

1. the working class
2. the middle class
3. the upper class
4. the upper-upper class (the “super rich”)

Answer: a Page: 289 LO: 1 and 4

• According to the theory presented in the text, which social class should have the strongest support for independent thinking as a goal of socialization?

1. people lower in class
2. people higher in class
3. rural dwellers
4. the upper-upper class (the “super rich”)

Answer: b Page: 289 LO: 1 and 4

• A test of the relationship between social class and socialization values was reported in the text. Which of the following was a result of this test?

1. socialization values are much stronger in the middle class
2. although only one relationship was significant, the pattern of percentages in the tables generally conform to theoretical expectations
3. socialization values increase as class increases
4. people in the lowest classes were overwhelmingly supportive of obedience as a socialization value.

Answer: b Page: 289-290 LO: 1 and 4

Test Problems

1. The city council is considering a law that would ban smoking in all public facilities. A sample has been selected from the community and tested for support of the ordinance. Is there a statistically significant relationship between age and support for the anti-smoking law? Use the five step model as a guide and write a sentence or two interpreting your results.

Age

Less than 40

More than 40

Support:

For

145

78

223

Against

103

169

272

248

247

495

2. Is support for the proposed anti-smoking law related to political party affiliation? Use the five step model as a guide and write a sentence or two interpreting your results.

Party

Democrat

Independent

Republican

Support

In Favor

36

23

17

76

Neutral

20

17

16

53

Opposed

10

18

36

64

66

58

69

193

Answers to Test Problems

1. Chi square = 36.11

2. Chi square = 0.08