Deck 16: Chi-Square

Question 1

Which of the following is required for chi-square?

A) homogeneity of variance
B) a normal population distribution
C) independent observations
D) interval or ratio level data

Answer 1

C

Question 2

The correct symbol for chi-square is __________.

A) r²
B) χ²
C) r
D) 1 - χ²

Answer 2

B

Question 3

The frequency values that would be expected if the null hypothesis is true are called ________________.

A) expected frequencies
B) observed frequencies
C) actual frequencies
D) anticipated frequencies

Answer 3

A

Question 4

Expected frequency is

A) what would be expected if the null hypothesis is false.
B) what would be expected if the null hypothesis is true.
C) the difference between observed and actual frequencies.
D) the difference between the chi-square value and the actual frequencies.

Question 5

Chi-square values will range from

A) -1 to +1
B) 0 to 1
C) 0 to positive infinity
D) 1 to positive infinity

Question 6

All of the following are true of chi-square tests except the following:

A) The expected frequencies for all categories should be a minimum of 5.
B) There are no negative chi-square values.
C) Each participant can contribute frequencies to only one category.
D) Chi-square is more likely to detect statistical significance than parametric tests.

Question 7

If no differences were found between observed and expected frequencies, then

A) the obtained chi-square value would be 0.
B) the null hypothesis would be rejected.
C) the null hypothesis would fail to be rejected.
D) Both "a" and "c" are correct.

Question 8

For a "no preference" goodness of fit chi-square test, the null hypothesis specifies that there

A) would be equal observed frequencies in every category.
B) would not be equal observed frequencies in every category.
C) would be equal expected frequencies in every category.
D) would not be equal expected frequencies in every category.

Question 9

The ___________ the difference between the observed and expected frequency, the _____________ the likely it is that the null hypothesis will be rejected.

A) greater; more
B) smaller; more
C) greater; less
D) The difference between observed and expected frequencies has no influence on whether the null hypothesis is rejected.

Question 10

In chi-square problems, the sum of

A) observed frequencies should be greater than the sum of expected frequencies.
B) observed frequencies should be less than the sum of expected frequencies.
C) observed frequencies should be equal to the sum of expected frequencies.
D) observed frequencies should be equal to the sum of expected frequencies only if the null hypothesis is true.

Question 11

The null hypothesis for a chi-square test of independence specifies

A) two variables to be independent.
B) two variables to be related.
C) observed frequencies to match the frequencies in the population.
D) equal frequencies in all categories.

Question 12

If is lower than ,

A) the null hypothesis can be rejected.
B) the null hypothesis cannot be rejected.
C) support has been gained for the alternative hypothesis.
D) Both "a" and "c" are correct.

Question 13

For a chi-square goodness of fit problem, df is determined by ___________.

A) (R - 1)(C - 1)
B) k - 1
C) n - 1
D) n - 2

Question 14

For a chi-square test of independence, df is determined by ___________.

A) (R- 1)(C - 1)
B) k - 1
C) n - 1
D) n - 2

Question 15

A market researcher is doing a blind taste test to determine if there are preferences among four different brands of chocolate. If n = 100, what is the expected frequency for each category?

A) 99
B) 3
C) 20
D) 25

Question 16

If is negative,

A) the observed frequencies were greater than the expected frequencies.
B) the expected frequencies were greater than the observed frequencies.
C) use a one-tailed test.
D) a mistake has been made.

Question 17

The expected frequency for a chi-square test of independence is determined by ______________.

A) (f_c)(f_r)/n
B) k - 1
C) n ÷ k
D) (R - 1)(C - 1)

Question 18

The expected frequency for a chi-square goodness of fit test for equal preferences is ______________.

A) (f_c)(f_r)/n
B) k - 1
C) n ÷ k
D) (R - 1)(C - 1)

Question 19

All of the following are true of chi-square tests except the following:

A) It measures the amount of discrepancy between observed and expected frequencies.
B) Participants can contribute to more than one category.
C) Nominal level data may be used.
D) Ordinal level data may be used.

Question 20

A one-way goodness of fit test examines one ________________.

A) category
B) sample
C) population
D) variable

Question 21

In determining df for a chi-square good of fit test, k refers to

A) row total.
B) column total.
C) the number of participants in each category.
D) the number of categories.

Question 22

A chi-square goodness of fit test was conducted with α = .05. The sample size was 100 spread over four categories. was 11.68 and was 7.815. Which of the following is correct for reporting the results?

A) Fail to reject H₀, χ² (4 df, n = 100) = 7.815, p < .05.
B) Reject H₀, χ² (df = 99) = 11.68, p < .05.
C) Reject H₀, χ² (3 df, n = 100) = 11.68, p < .05.
D) Fail to reject H₀, χ² (3 df, n = 100) = 7.815, p > .05.

Question 23

A chi-square goodness of fit test was conducted with α = .01. The sample size was 180 spread over six categories. was 12.94 and was 15.086. Which of the following is correct for reporting the results?

A) Reject H₀, χ² (5 df, n = 180) = 12.94, p < .01.
B) Fail to reject H₀, χ² (5 df, n = 180) = 12.94, p > .01.
C) Fail to reject H₀, χ² (5 df, n = 180) = 15.086, p > .01.
D) Reject H₀, χ² (n = 179) = 15.86, p < .01.

Question 24

A researcher was interested if there is a relationship between marital status (single or married) and type of television program preferred (drama, comedy, action, or documentary). 48 married and 52 single individuals indicted their preferred program type. A chi-square test of independence was conducted. α = .05, = 8.14, and . Which of the following is correct for reporting the results?

A) Reject H₀, χ² (3 df, n = 100) = 8.14, p < .05.
B) Reject H₀, χ² (7 df, n = 100) = 8.14, p < .05.
C) Reject H₀, χ² (df = 98) = 8.14, p < .05.
D) Fail to reject H₀, χ² (df = 98) = 7.815, p > .05.

Question 25

A one-way chi-square goodness of fit test has df = 5 and n = 250. The variable being examined consisted of __________ categories.

A) 4
B) 5
C) 6
D) 50

Question 26

If the alternative hypothesis of a chi-square test is supported, should be

A) 0
B) > 0
C) < 0
D) either "b" or "c."

Question 27

The alternative hypothesis for a chi-square test of independence is that

A) observed frequencies will match the frequencies of the population.
B) observed frequencies will not be evenly distributed among categories.
C) two variables are related.
D) two variables are not related.

Question 28

The chi-square _____________ is used to determine if there is a relationship between two variables.

A) test of independence
B) goodness of fit test for no preference
C) goodness of fit test for known proportions
D) test of predicted frequencies

Question 29

The null hypothesis for a chi-square goodness of fit test for known proportions specifies that

A) the variables are independent.
B) the variables are not independent.
C) the observed frequencies match the frequencies in the population.
D) the observed frequencies do not match the frequencies in the population.

Question 30

In a chi-square test, the sum of the observed frequencies should be equal to

A) the sum of the expected frequencies.
B) n
C) χ²
D) Both "a" and "b" are correct.

Question 31

Under what conditions would you use a nonparametric test such as chi-square?

Question 32

With what scales of measurement can chi-square be used?

Question 33

What is meant by observed frequencies?

Question 34

What is meant by expected frequencies?

Question 35

Indicate the correct formulas for df and f_e for the chi-square tests below.
a. Goodness of fit for known proportions
b. Goodness of fit for no preference
c. Test of independence

Question 36

Participants in a national survey were asked if they believe that public school teachers are paid too much, the right amount, or too little. The results were as follows:
Too much - 16%
The right amount - 23%
Too little - 57%
No response - 4%
A random sample of n = 328 residents of a particular community was asked about the same issue. What would the expected frequencies be for each category if the null hypothesis is true?

Question 37

A random sample of 76 shoppers indicate their preference in a taste test for the following brands of smooth peanut butter: Georgia's Best, Tasty's, Eversmooth, and Uncle Jim's. If a chi-square goodness of fit test for equal preferences is used, what are the expected frequencies if the null hypothesis is true?

Question 38

97 males and 100 females, all aged 25 to 35, were asked about their satisfaction with their current weight. The results are in the table below. If a chi-square test is used to determine if there is a relationship between gender and weight satisfaction, what are the expected frequencies for each category?

Question 39

A marketing agency reported the following market share percentages for last year's top selling brands of yogurt: Brand A - 28%; Brand B - 21%; Brand C - 18%; Brand D - 12%; Other - 21%. Since some companies have recently enhanced their products, the agency conducted a survey to determine if the yogurt preferences reported this year match last year's market shares. The distribution of yogurt preferences for the 240 participants of the current study were as follows: Brand A - 60; Brand B - 77; Brand C - 48; Brand D - 26, and Other - 29. Conduct a chi-square goodness of fit test for known proportions using α = .05.

Question 40

A candle manufacturer wanted to know which of four fragrances would be preferred for its new line of candles: vanilla, cinnamon, lavender, or eucalyptus. A random sample of 116 candle shoppers were asked their preferences with the following results:
Vanilla - 32
Cinnamon - 14
Lavender - 37
Eucalyptus - 33
Conduct a chi-square goodness of fit test for equal preference using α = .05.

Question 41

A history instructor wondered about the effectiveness of graded quizzes over material that students were supposed to read prior to class. For one of his sections, quizzes were administered and graded. For another section, the same quizzes were administered but instead of counting toward their grade, students simply used them as practice for exams. Final grade distributions for both sections are shown in the table below. Is there a relationship between final grades and whether quizzes are graded or used for practice? Conduct a chi-square test of independence using α = .05.