Question 1

Which of the following accurately describes the chi-square test for goodness of fit?​

Accepted Answer

The chi-square test for goodness of fit is used to determine how well observed frequencies match expected frequencies in one categorical variable, similar to how a single-sample t-test compares a sample mean to a population mean.

Question 2

What happens to the critical value for a chi-square test if the size of the sample is increased?​

Accepted Answer

The critical value for a chi-square test is determined by the degrees of freedom and the level of significance, not the sample size. However, the number of categories does affect the degrees of freedom. As the number of categories increases, the degrees of freedom also increase, allowing for more variability and a lower critical value.

Question 3

Which of the following accurately describes the observed frequencies for a chi-square test?​

Accepted Answer

Observed frequencies in a chi-square test refer to the actual counts of occurrences in each category, which are always whole numbers since you cannot observe a fraction or a negative amount of occurrences.

Question 4

For a given alpha level,what happens to the critical value for a chi-square test if the number of categories is increased?​

Accepted Answer

The critical value for a chi-square test increases as the number of categories increases because the degrees of freedom (calculated as the number of categories minus one) increase, and the critical value is determined based on the degrees of freedom and the alpha level.

Question 5

The term expected frequencies refers to the frequencies ____.​

Accepted Answer

Expected frequencies are computed from the null hypothesis, which assumes that there is no significant difference between the observed frequencies and what we would expect to see by chance.

Question 6

How does the difference between f_e and f_o influence the outcome of a chi-square test?

Accepted Answer

The larger the difference between the observed and expected values (f_e and f_o respectively), the larger the value of chi-square. A larger chi-square value indicates a greater deviation from the expected values and increases the likelihood of rejecting the null hypothesis. Therefore, the best choice is A.

Question 7

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

Accepted Answer

A chi-square statistic cannot be negative. A negative value indicates an error in calculation or interpretation.

Question 8

For a fixed level of significance,the critical value for the chi-square will ____.​

Accepted Answer

The critical value for the chi-square increases as the degrees of freedom (df) value increases. This is because for larger df values, the distribution becomes less skewed and the tails become less spread out, leading to a larger critical value requirement for rejection of the null hypothesis. The sample size does not directly affect the critical value for the chi-square.

Question 9

​Ten years ago,only 15% of the U.S.population consisted of people more than 65 years old.A researcher plans to use a sample of n = 300 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?

Accepted Answer

The expected frequency is calculated by multiplying the sample size (n = 300) by the proportion of the population in the category of interest (15% or 0.15). Thus, 300 * 0.15 = 45.

Question 10

Which of the following best describes the possible values for a chi-square statistic?​

Accepted Answer

Chi-square is always positive because it is the sum of squared differences. However, it can contain fractions or decimal values.

Question 11

A chi-square test for goodness of fit has df = 2.How many categories were used to classify the individuals in the sample?​

Accepted Answer

The degrees of freedom (df) for a chi-square test for goodness of fit is calculated as the number of categories minus one. Therefore, if df = 2, then there were 3 categories (2 + 1 = 3).

Question 12

What is evaluated by the chi-square test for goodness of fit?​

Accepted Answer

The chi-square test for goodness of fit is used to evaluate whether the observed frequencies of a categorical variable match the expected frequencies based on a hypothesized distribution. Therefore, it evaluates the shape or proportions for a population distribution.

Question 13

The term observed frequencies refers to the frequencies ____.​

Accepted Answer

Observed frequencies refer to the frequencies that are found in the sample data. These frequencies are observed or measured in the actual data collected from the sample population.

Question 14

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?​

Accepted Answer

With four categories (brands of pizza) and using a chi-square test for goodness of fit, the degrees of freedom (df) are calculated as the number of categories minus one, which is 4 - 1 = 3. At an alpha level of .05, the critical value for df = 3 is 7.81. Therefore, to reject the null hypothesis, the chi-square statistic needs to be greater than 7.81.

Question 15

​Which of the following accurately describes the chi-square distribution?

Accepted Answer

The chi-square distribution is a positively skewed distribution with all values greater than or equal to zero. It is commonly used in hypothesis testing for comparing observed frequencies to expected frequencies.

Question 16

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?​

Accepted Answer

The degrees of freedom (df) for a chi-square test for goodness of fit is calculated as the number of categories minus one. Therefore, with four categories, df = 4 - 1 = 3.

Question 17

What conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?​

Accepted Answer

A chi-square statistic near zero indicates that there is a good fit between the sample data and the null hypothesis, meaning that the observed frequencies are close to the expected frequencies. This suggests that any differences between the observed and expected frequencies are likely due to chance, rather than a significant deviation from the null hypothesis.

Question 18

What values are specified by the null hypothesis for the chi-square test for goodness of fit?​

Accepted Answer

The null hypothesis for the chi-square test for goodness of fit specifies the expected proportions for the entire population, not just for a sample or specific frequencies.

Question 19

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

Accepted Answer

A large value for the chi-square statistic indicates a poor fit between the observed values and the null hypothesis, which means that the sample data do not match the null hypothesis. This suggests that the observed values may have been influenced by some other factor or that the null hypothesis is not a good representation of the population being studied.

Question 20

Which of the following accurately describes the expected frequencies for a chi-square test?​

Accepted Answer

The expected frequencies in a chi-square test can contain fractions or decimal values.

Quiz 17: The Chi-Square Statistic: Tests for Goodness of Fit and Independence

Which of the following accurately describes the chi-square test for goodness of fit?​

What happens to the critical value for a chi-square test if the size of the sample is increased?​

Which of the following accurately describes the observed frequencies for a chi-square test?​

For a given alpha level,what happens to the critical value for a chi-square test if the number of categories is increased?​

The term expected frequencies refers to the frequencies ____.​

How does the difference between fe and fo influence the outcome of a chi-square test?​

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

For a fixed level of significance,the critical value for the chi-square will ____.​

Which of the following best describes the possible values for a chi-square statistic?​

A chi-square test for goodness of fit has df = 2.How many categories were used to classify the individuals in the sample?​

What is evaluated by the chi-square test for goodness of fit?​

The term observed frequencies refers to the frequencies ____.​

​Which of the following accurately describes the chi-square distribution?

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?​

What conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?​

What values are specified by the null hypothesis for the chi-square test for goodness of fit?​

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

Which of the following accurately describes the expected frequencies for a chi-square test?​

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

What happens to the critical value for a chi-square test if the size of the sample is increased?

Which of the following accurately describes the observed frequencies for a chi-square test?

For a given alpha level,what happens to the critical value for a chi-square test if the number of categories is increased?

The term expected frequencies refers to the frequencies ____.

How does the difference between f_e and f_o influence the outcome of a chi-square test?

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

For a fixed level of significance,the critical value for the chi-square will ____.

Which of the following best describes the possible values for a chi-square statistic?

A chi-square test for goodness of fit has df = 2.How many categories were used to classify the individuals in the sample?

What is evaluated by the chi-square test for goodness of fit?

The term observed frequencies refers to the frequencies ____.

Which of the following accurately describes the chi-square distribution?

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?

What conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?

What values are specified by the null hypothesis for the chi-square test for goodness of fit?

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

Which of the following accurately describes the expected frequencies for a chi-square test?