Question 1

A null hypothesis of "no association" is rejected at the 0.01 level. Which of the following is a valid conclusion?

Accepted Answer

D

Question 2

A teacher wants to determine if students who use a new study method improve their performance. Which of the following would be the best example of a null hypothesis used to formally test this idea?

Accepted Answer

The null hypothesis typically states that there is no effect or no difference. In this context, it would mean that students using the new study method do no better than the typical class average.

Question 3

If an observed test statistic is within the "critical region," what should we conclude?

Accepted Answer

The critical region is defined as the area in the tails of the sampling distribution where unlikely sample outcomes occur, leading to the rejection of the null hypothesis.

Question 4

What may be concluded if the test statistic falls in the critical region in a test of significance?

Accepted Answer

If the test statistic falls in the critical region, it indicates that there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

Question 5

If a null hypothesis that is in fact true has been rejected, then which of the following is indicated?

Accepted Answer

A Type I error occurs when a true null hypothesis is incorrectly rejected.

Question 6

When a researcher chooses alpha, what is he or she essentially selecting the probability of?

Accepted Answer

Alpha is the probability of committing a Type I error, which occurs when the null hypothesis is incorrectly rejected.

Question 7

What is the alpha level at which a researcher would most likely reject the null hypothesis?

Accepted Answer

The answer of What is the alpha level at which...

Question 8

Which of the following is a researcher more likely to do at a higher alpha level?

Accepted Answer

The answer of Which of the following is a researcher...

Question 9

What is the assumed sampling distribution for a chi square test?

Accepted Answer

The chi square test does not assume a specific sampling distribution; it is based on the chi square distribution itself, which is used to test hypotheses about categorical data.

Question 10

Suppose that both variables in a bivariate table have four categories. How many cells will the table have?

Accepted Answer

A bivariate table with two variables, each having four categories, will have 4 x 4 = 16 cells.

Question 11

Which of the following is an example of a polytomous variable that could be depicted in a bivariate table?

Accepted Answer

A polytomous variable is one that can take on more than two categories. Option C includes multiple categories (working, self-employed, retired, unemployed), making it a polytomous variable suitable for depiction in a bivariate table.

Question 12

A researcher analyzes data from a bivariate table with a chi square test. The two variables in the table are sex (man, woman) and political affiliation (NDP, Liberal, Conservative). What does the null hypothesis state?

Accepted Answer

The null hypothesis in a chi-square test for independence states that the two variables are independent, meaning there is no association between sex and political affiliation.

Question 13

Which of these terms refers to cell frequencies computed under the assumption that the null hypothesis is true?

Accepted Answer

Expected frequencies are calculated based on the assumption that the null hypothesis is true, and they represent the theoretical distribution of frequencies in a contingency table.

Question 14

A chi square test concludes that home owners and home renters differed in their likelihood of having a registered retirement savings plan (RRSP). What would characterize the expected and observed frequencies of these variables in the bivariate table?

Accepted Answer

A chi-square test indicates a significant difference when the observed frequencies differ greatly from the expected frequencies, suggesting an association between the variables.

Question 15

Which of the following would summarize the relationship between f_e (expected frequencies) and f_o (observed frequencies) if we reject the null hypothesis in a chi square test?

Accepted Answer

When we reject the null hypothesis in a chi-square test, it indicates that there is a significant difference between the expected frequencies (f_e) and the observed frequencies (f_o), meaning they are not similar and one is much greater than the other.

Question 16

If row marginal = 75, column marginal = 12, and n = 50, what is the expected frequency?

Accepted Answer

Expected frequency = (row marginal * column marginal) / n = (75 * 12) / 50 = 18

Question 17

The observed row and column marginals of a bivariate table are 22 and 40 respectively. What can be concluded about the total expected values for the rows and columns?

Accepted Answer

The total expected values for the rows and columns in a bivariate table must match the observed row and column marginals, which are 22 and 40, respectively.

Question 18

How are degrees of freedom computed for a chi square test?

Accepted Answer

Degrees of freedom for a chi-square test are computed as (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table.

Question 19

Where would the critical region begin for a chi square test with the alpha level set at 0.05 and with 8 degrees of freedom?

Accepted Answer

For a chi-square test with 8 degrees of freedom and an alpha level of 0.05, the critical value is 15.51, which marks the beginning of the critical region.

Question 20

How is the shape of sampling distribution for chi square different from that of the Z and the t distributions?

Accepted Answer

The chi-square distribution is positively skewed, especially for small degrees of freedom, unlike the Z and t distributions which are symmetric.

Quiz 7: Hypothesis Testing With Nominal and Ordinal Variables: CHI Square

A null hypothesis of "no association" is rejected at the 0.01 level. Which of the following is a valid conclusion?

A teacher wants to determine if students who use a new study method improve their performance. Which of the following would be the best example of a null hypothesis used to formally test this idea?

If an observed test statistic is within the "critical region," what should we conclude?

What may be concluded if the test statistic falls in the critical region in a test of significance?

If a null hypothesis that is in fact true has been rejected, then which of the following is indicated?

When a researcher chooses alpha, what is he or she essentially selecting the probability of?

What is the alpha level at which a researcher would most likely reject the null hypothesis?

Which of the following is a researcher more likely to do at a higher alpha level?

What is the assumed sampling distribution for a chi square test?

Suppose that both variables in a bivariate table have four categories. How many cells will the table have?

Which of the following is an example of a polytomous variable that could be depicted in a bivariate table?

A researcher analyzes data from a bivariate table with a chi square test. The two variables in the table are sex (man, woman) and political affiliation (NDP, Liberal, Conservative) . What does the null hypothesis state?

Which of these terms refers to cell frequencies computed under the assumption that the null hypothesis is true?

A chi square test concludes that home owners and home renters differed in their likelihood of having a registered retirement savings plan (RRSP) . What would characterize the expected and observed frequencies of these variables in the bivariate table?

Which of the following would summarize the relationship between f_e (expected frequencies) and f_o (observed frequencies) if we reject the null hypothesis in a chi square test?

If row marginal = 75, column marginal = 12, and n = 50, what is the expected frequency?

The observed row and column marginals of a bivariate table are 22 and 40 respectively. What can be concluded about the total expected values for the rows and columns?

How are degrees of freedom computed for a chi square test?

Where would the critical region begin for a chi square test with the alpha level set at 0.05 and with 8 degrees of freedom?

How is the shape of sampling distribution for chi square different from that of the Z and the t distributions?

Quiz 7: Hypothesis Testing With Nominal and Ordinal Variables: CHI Square

A null hypothesis of "no association" is rejected at the 0.01 level. Which of the following is a valid conclusion?

A teacher wants to determine if students who use a new study method improve their performance. Which of the following would be the best example of a null hypothesis used to formally test this idea?

If an observed test statistic is within the "critical region," what should we conclude?

What may be concluded if the test statistic falls in the critical region in a test of significance?

If a null hypothesis that is in fact true has been rejected, then which of the following is indicated?

When a researcher chooses alpha, what is he or she essentially selecting the probability of?

What is the alpha level at which a researcher would most likely reject the null hypothesis?

Which of the following is a researcher more likely to do at a higher alpha level?

What is the assumed sampling distribution for a chi square test?

Suppose that both variables in a bivariate table have four categories. How many cells will the table have?

Which of the following is an example of a polytomous variable that could be depicted in a bivariate table?

A researcher analyzes data from a bivariate table with a chi square test. The two variables in the table are sex (man, woman) and political affiliation (NDP, Liberal, Conservative) . What does the null hypothesis state?

Which of these terms refers to cell frequencies computed under the assumption that the null hypothesis is true?

A chi square test concludes that home owners and home renters differed in their likelihood of having a registered retirement savings plan (RRSP) . What would characterize the expected and observed frequencies of these variables in the bivariate table?

Which of the following would summarize the relationship between fe (expected frequencies) and fo (observed frequencies) if we reject the null hypothesis in a chi square test?

If row marginal = 75, column marginal = 12, and n = 50, what is the expected frequency?

The observed row and column marginals of a bivariate table are 22 and 40 respectively. What can be concluded about the total expected values for the rows and columns?

How are degrees of freedom computed for a chi square test?

Where would the critical region begin for a chi square test with the alpha level set at 0.05 and with 8 degrees of freedom?

How is the shape of sampling distribution for chi square different from that of the Z and the t distributions?

Which of the following would summarize the relationship between f_e (expected frequencies) and f_o (observed frequencies) if we reject the null hypothesis in a chi square test?