Statistics Chapter 14

A researcher selects a sample of 110 participants and computes the following phi correlation coefficient: mc032-1.jpg = .31. What is the value of X^2? a. 3.84 b. 34.10 c. 10.57 d. There is not enough information to answer this question.

c. 10.57

A researcher records the frequency of participants selecting one of four new slogans for an advertising campaign. If it was expected that among 200 people polled there would be no preference for any one slogan, then what was the expected frequency for each slogan? a. 25 people b. 100 people c. 50 people d. 200 people

c. 50 people

A researcher computes a 2 × 4 chi-square test for independence. What are the degrees of freedom for this test? a. 2 b. 4 c. 8 d. 3

d. 3

A researcher compares the frequency of participants who sleep primarily on their stomach, back, or side during the night. What is the critical value for a chi-square goodness-of-fit test at a .05 level of significance? a. 3 b. 3.84 c. 2 d. 5.99

d. 5.99

A researcher reports the following results for a chi-square test for independence: x^2 (1) = 5.386, p < .05 (V = .22). What is the maximum number of levels that an independent variable could have had? a. 2 b. 4 c. 3 d. 1

a. 2

A researcher computes a 2 × 3 chi-square test for independence. What is the critical value for this test at a .05 level of significance? a. 5.99 b. 12.59 c. 7.81 d. 3.84

a. 5.99

A researcher computes a 3 × 5 chi-square test for independence. What are the degrees of freedom for this test? a. 8 b. 3 c. 15 d. 5

a. 8

To appropriately interpret the chi-square goodness-of-fit test, it is necessary to compare differences ______. a. at each level of the categorical variable b. within and between expected frequencies c. across the levels of the categorical variable

a. at each level of the categorical variable

When computing a chi-square goodness-of-fit test, the frequency expected in a given cell should never be less than ______. a. five b. the number of cells c. the frequency observed d. the sample size

a. five

One way a researcher can correct for having expected frequencies smaller than five is to increase the sample size such that ______. a. it is five times larger than the number of cells b. it is three times larger than the number of cells c. it is seven times smaller than the number of cells d. it is equal to the number of cells

a. it is five times larger than the number of cells

A local ice cream shop wants to see if they should promote a new swizzleberry swirl or creamsicle flavored drink. In order to determine which one to promote, they took a sample of 80 patrons and asked them to choose which they preferred. The one that is significantly preferred over the other (at a .05 level of significance) will be promoted. It is expected that an equal number of patrons will choose each flavor. Based on the observed frequencies given below, what is the decision for this test? a. promote the creamsicle flavored drink b. do not promote any flavored drinks c. There is not enough information to answer this question. d. promote the swizzleberry swirl flavored drink

a. promote the creamsicle flavored drink

We compute the frequency expected in each category using known ______ stated in the null hypothesis. a. proportions b. variances c. effect sizes d. hypothesis tests

a. proportions

The degrees of freedom for a chi-square test for independence test are ______. a. n - 1 b. (k1-1)(k2-1) c. k - 1 d. (k - 1)(n - 1)

b. (k1-1)(k2-1)

To compute the expected frequencies for a chi-square test for independence, we use which of the following formulas? a. k - 1 b. (row total × column total)/grand total c. (row total + column total)/grand total d. p(n)

b. (row total × column total)/grand total

A researcher computes a 4 × 6 chi-square test for independence with a sample of 120 participants, with mc036-1.jpg = 14.79. What is the effect size for this result? a. .12 b. .20 c. .35 d. .04

b. .20

A researcher computes a 3 × 4 chi-square test for independence with a sample of 50 participants, with mc035-1.jpg = 8.43. What is the effect size for this result? a. .17 b. .29 c. .08 d. .41

b. .29

A researcher selects a sample of 80 people and records the frequency of participants choosing a low-, moderate-, or high-calorie dessert in a buffet. What are the degrees of freedom for this chi-square goodness-of-fit test? a. 3 b. 2 c. 80 d. 79

b. 2

A researcher conducts a chi-square goodness-of-fit test in which k = 5. What is the critical value for this test at a .05 level of significance? a. 5 b. 9.49 c. 4 d. 11.07

b. 9.49

A researcher tests whether levels of education and income levels are related. In this study, he observes the following frequencies. If he computes a chi-square test for independence at a .05 level of significance, then what is the decision for this test? a. Both B and C are appropriate. b. Education and income level are related. c. Education and income level are independent. d. Education and income level are not related.

b. Education and income level are related.

What is the key assumption for a chi-square goodness-of-fit test? a. The population is normally distributed. b. Observed frequencies are independently recorded in each cell. c. Expected frequencies are homogeneous. d. all of these

b. Observed frequencies are independently recorded in each cell.

To appropriately interpret the chi-square goodness-of-fit test, it is necessary to compare differences ______ of the categorical variable. a. outside the levels b. at each level c. between the levels d. across the levels

b. at each level

A researcher can correct for having expected frequencies smaller than five by ______. a. decreasing the observed frequency b. both A and B c. increasing the number of cells d. increasing the sample size

b. both A and B

Which of the following is recorded using a chi-square goodness-of-fit test and a chi-square test for independence? a. frequency expected b. both B and C c. frequency observed d. variance

b. both B and C (frequency expected and frequency observed)

Which of the following is an example of a nonparametric test? a. the t tests b. chi-square test c. Pearson correlation d. analysis of variance

b. chi-square test

Many nonparametric tests are called ______ because they make no assumptions regarding the shape of the distribution in the population. a. significance-free tests b. distribution-free tests c. skewed-distribution tests d. parametric tests

b. distribution-free tests

A chi-square goodness-of-fit test shows that the frequencies observed equal those that were expected. Hence, the value of the test statistic is ______. a. small; less than the critical value but not necessarily equal to 0 b. equal to 0 c. large; greater than the critical value d. less than 0

b. equal to 0

The interpretation of a 2 × 2 chi-square test for independence is similar to what other type of statistical test? a. two-independent-sample t test b. phi correlation coefficient c. 2 × 2 analysis of variance d. goodness-of-fit chi-square test

b. phi correlation coefficient

A researcher conducts a chi-square goodness-of-fit test in which k = 2 and mc002-1.jpg = 3.98. What is the decision for this test at a .05 level of significance? a. There is not enough information to answer this question. b. reject the null hypothesis c. retain the null hypothesis

b. reject the null hypothesis

A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected. Hence, the decision was to ______. a. No decision was made. b. retain the null hypothesis c. reject the null hypothesis

b. retain the null hypothesis

A researcher conducts a chi-square goodness-of-fit test in which k = 3 and x^2 = 4.32. What is the decision for this test at a .05 level of significance? a. There is not enough information to answer this question. b. retain the null hypothesis c. reject the null hypothesis

b. retain the null hypothesis

A researcher conducts two chi-square tests. The 2 × 2 chi-square was mc008-1.jpg = 3.92. The 2 × 3 chi-square was mc008-2.jpg = 5.92. Which chi-square test resulted in a decision to reject the null hypothesis at a .05 level of significance? a. the 2 × 3 chi-square b. the 2 × 2 chi-square c. Both chi-square tests result in a decision to reject the null hypothesis. d. None; both chi-square tests result in a decision to retain the null hypothesis.

b. the 2 × 2 chi-square

As a general rule, the larger the degrees of freedom for a chi-square test, ______. a. the larger the level of significance will be b. the larger the critical value will be c. the smaller the critical value will be d. the smaller the level of significance will be

b. the larger the critical value will be

A researcher computes a 2 × 2 chi-square test for independence. What is the critical value for this test at a .05 level of significance? a. 7.81 b. 5.99 c. 3.84 d. 9.49

c. 3.84

Which of the following measures of effect size can be reported with a 3 × 4 chi-square test for independence? a. proportion of variance b. the phi coefficient c. Cramer's V d. all of these

c. Cramer's V

A researcher conducts two chi-square tests. The 2 × 2 chi-square was x^2 = 3.82. The 2 × 3 chi-square was x^2= 5.02. Which chi-square test resulted in a decision to reject the null hypothesis at a .05 level of significance? a. the 2 × 2 chi-square b. Both chi-square tests result in a decision to reject the null hypothesis. c. None; both chi-square tests result in a decision to retain the null hypothesis. d. the 2 × 3 chi-square

c. None; both chi-square tests result in a decision to retain the null hypothesis.

What is a key distinction between parametric tests and nonparametric tests in terms of scales of measurement? a. There is no distinction; both types of tests are used to analyze data on any scale of measurement. b. Parametric tests are used for ordinal or interval data, whereas nonparametric tests are used for nominal data only. c. Parametric tests are used for interval and ratio data, whereas nonparametric tests are used for nominal and ordinal data. d. Parametric tests are used for ordinal and nominal data, whereas nonparametric tests are used for interval and ratio data.

c. Parametric tests are used for interval and ratio data, whereas nonparametric tests are used for nominal and ordinal data.

A researcher asks participants to taste each of three meals and to choose the one they like best. The same foods are in each meal, expect for the calorie total of the meal (which is low, moderate, or high calorie). Based on the observed frequencies given below, what is an appropriate conclusion for this test at a .05 level of significance? a. Participants liked the high calorie meal more than the low-calorie meal. b. Participants liked the low-calorie meal less than the moderate calorie meal. c. Participants liked the high calorie meal more than was expected. d. all of these

c. Participants liked the high calorie meal more than was expected.

Which of the following is a statistical procedure used to test hypotheses about the discrepancy between the observed and expected frequencies in two or more nominal categories? a. one-way ANOVA b. analysis of regression c. chi-square test d. all of these

c. chi-square test

The degrees of freedom for a chi-square goodness-of-fit test are ______. a. (k - 1)(n - 1) b. n - 1 c. k - 1 d. mc011-1.jpg

c. k - 1

A researcher computes a 4 × 4 chi-square test for independence and estimates the following effect size: V = .36. This effect size is ______. a. small b. medium c. large

c. large

A researcher reports the following results for a chi-square goodness-of-fit test: x^2 (1) = 5.386, p < .05 (V = .22). How many groups were observed? a. 3 b. 1 c. 4 d. 2

d. 2

A chi-square goodness-of-fit test leads to a decision to retain the null hypothesis. Which of the following correctly explains this decision? a. Frequencies observed were significantly different from frequencies expected across the levels of the categorical variable. b. Frequencies observed were significantly different from frequencies expected at each level of the categorical variable. c. Frequencies observed were significantly different from frequencies expected within and between expected frequencies. d. Frequencies observed were statistically similar to the frequencies expected at each level of the categorical variable.

d. Frequencies observed were statistically similar to the frequencies expected at each level of the categorical variable.

A researcher tests whether job security and life satisfaction are related. In this study, he observes the following frequencies. If he computes a test for independence at a .05 level of significance, then what is the decision for this test? a. Both A and B are appropriate. b. Job security and job satisfaction are dependent. c. Job security and job satisfaction are related. d. Job security and job satisfaction are independent.

d. Job security and job satisfaction are independent.

Which of the following is a key assumption for a chi-square goodness-of-fit test? a. The proportion in each cell is equal to zero. b. There is no mean difference between groups. c. The variance between groups is equal. d. The observed frequencies are independently recorded in each cell.

d. The observed frequencies are independently recorded in each cell.

The observed frequencies can be summarized ______. a. in a table b. in a figure c. in the main text d. all of these

d. all of these

To summarize the chi-square goodness-of-fit test, which of the following is reported? a. test statistic b. p value c. degrees of freedom d. all of these

d. all of these

Which of the following is an appropriate measure of effect size for a 2 × 2 chi-square test for independence? a. proportion of variance b. the phi coefficient c. Cramer's V d. all of these

d. all of these

Which of the following is an example of a parametric test? a. analysis of variance b. one-sample t test c. Pearson correlation d. all of these

d. all of these

One way a researcher can correct for having expected frequencies smaller than five is to increase the levels of the categorical variable such that the number of levels ______. a. is equal to the sample size b. is minimal c. is less than five d. is greater than four

d. is greater than four

If the expected frequencies equal to observed frequencies for a chi-square test for independence, what do we conclude? a. the degrees of freedom for the test are equal to 0 b. the frequencies observed fit well with the frequencies expected c. both B and C d. the test statistic value is equal to 0

d. the test statistic value is equal to 0