Exam 15: The Chi-Square Statistic: Tests for Goodness of Fit and Independence

If other factors are held constant,increasing the sample size for a chi-square test for independence will increase the likelihood of rejecting the null hypothesis.

What is indicated by a large value for the chi-square statistic?

A researcher is interested in consumer preferences among three brands of yogurt.A sample of 90 people is obtained,and each individual is asked to taste each brand and then select his/her favorite.The resulting frequency data are as follows: Brand A Brand B Brand C 37 21 32 Do the data indicate any significant preferences among the three brands? Test at the .05 level of significance.

Which of the following is a basic assumption for a chi-square hypothesis test?

Cramér's V is used to evaluate effect size for the chi-square test for independence whenever the test has df = 1.

Ten years ago,only 20% of the U.S.population consisted of people more than 65 years old.A researcher plans to use a sample of n = 200 people to determine whether the population distribution has changed during the past ten years.If a chi-square test is used to evaluate the data,what is the expected frequency for the older-than-65 category?

Which of the following accurately describes the chi-square test for independence?

A chi-square test for goodness of fit is used to examine the distribution of individuals across four categories,and a chi-square test for independence is used to examine the distribution of individuals across the six categories in a 2×3 matrix of categories.Which test has the larger value for df?

A researcher selects a sample of 100 people to investigate the relationship between gender (male/female)and registering to vote.The sample consists of 40 females,of whom 30 are registered voters,and 60 males,of whom 40 are registered voters.If these data were used for a chi-square test for independence,what is the observed frequency for registered males?

A sample of 100 people is classified by gender (male/female)and by whether they are registered voters.The sample consists of 80 females and 20 males,and has a total of 60 registered voters.If these data are used for a chi-square test for independence,what is the total number of females for the expected frequencies?

A researcher used a sample of n = 60 individuals to determine whether there are any preferences among four brands of pizza.Each individual tastes all four brands and selects his/her favorite.If the data are evaluated with a chi-square test for goodness of fit using α = .05,then how large does the chi-square statistic need to be to reject the null hypothesis?

A researcher is examining preferences among four new flavors of ice cream.A sample of n = 80 people is obtained.Each person tastes all four flavors and then picks his/her favorite.The distribution of preferences is as follows. Ice Cream Flavor A B C D 12 18 28 22 Do these data indicate any significant preferences among the four flavors? Test at the .05 level of significance.

For a fixed level of significance,how is the critical value for chi-square related to degrees of freedom?

The chi-square test for goodness of fit evaluates the distribution for one variable,and the test for independence evaluates the relationship between two variables.

A researcher is interested in the relationship between birth order and personality.A sample of n = 100 people is obtained,all of whom grew up in families as one of three children.Each person is given a personality test,and the researcher also records the person's birth-order position (1st born,2nd,or 3rd).The frequencies from this study are shown in the following table.On the basis of these data,can the researcher conclude that there is a significant relation between birth order and personality? Test at the .05 level of significance.

A researcher obtains a negative value for chi-square statistic.What can you conclude because the value is negative?

For a fixed level of significance,the critical value for chi-square increases as the degrees of freedom increase.

A chi-square test for independence is being used to evaluate the relationship between two variables,one of which is classified into 3 categories and the second of which is classified into 4 categories.What is the df value for the chi-square statistic?

A sample of n = 100 people is classified into four categories.If the results are evaluated with a chi-square test for goodness of fit,what is the df value for the chi-square statistic?

A chi-square test for independence is being used to evaluate the relationship between two variables.If the test has df = 3,what can you conclude about the two variables?