Question 1

ANOVA involving only one grouping variable is often referred to as one-way ANOVA.

Accepted Answer

One-way ANOVA involves only one grouping variable, which is why it is called "one-way".

Question 2

If 25 of the 35 females in a research study agree with a statement, and 15 of the 35 males agree with this statement, the expected value for males-agree is _____.

Accepted Answer

The expected value is the number of individuals that we would expect to agree if the proportions of males and females agreeing were equal. Since there are 35 participants in total and 25 are female, the expected proportion of males in the study is (35-25)/35 = 10/35 = 2/7. Therefore, we can multiply the total number of males (35-25 = 10) by this proportion to find the expected number of males who agree with the statement: 
(2/7) * 10 = 20/7 ≈ 2.86
Since we can't have a fraction of a person, we round to the nearest whole number, which gives us an expected value of 3. Therefore, the best choice is B (20).

Question 3

The formula for the chi-square test uses _____.

Accepted Answer

The chi-square test compares observed frequencies with expected frequencies in order to test the independence of two variables. The formula for the test uses the observed frequencies and the expected frequencies, making choice A the correct answer. Choices B, C and D are not relevant to the chi-square test.

Question 4

A(n) _____ is a test for hypotheses stating that the mean scores from some interval- or ratio-scaled variable group based on some less-than interval classificatory variable are not the same.

Accepted Answer

The independent samples t-test is specifically designed for testing differences in means between two groups, where the data is interval or ratio scaled. It is most appropriate for this scenario among the options given.

Question 5

The null hypothesis for an ANOVA test comparing the means of three groups is: m₁_¹m₂_¹m_3.

Accepted Answer

The null hypothesis for an ANOVA test comparing the means of three groups should be that there is no significant difference between the group means. The provided hypothesis seems to be a combination of group means and the interaction between the independent variables and is not a valid null hypothesis for ANOVA.

Question 6

Suppose that you used a 9-point rating scale and that you wanted to compare men who had an annual income over $50,000 (Group 1) with men who had an annual income less than or equal to $50,000 (Group 2) on their liking of a new product. If you studied 40 men in Group 1 and they have a mean of 7 and a standard deviation of 2.5, while the 35 men in Group 2 have a mean of 5 and a standard deviation of 1.4, what is the approximate value of t using the t-test?

Accepted Answer

The answer of Suppose that you used a 9-point rating...

Question 7

The F-test partitions the total variance into within-group variance and between-group variance.

Accepted Answer

The F-test is used in analysis of variance (ANOVA) to compare the means of two or more groups. It calculates the ratio of between-group variance to within-group variance. Therefore, it partitions the total variance into these two components.

Question 8

A researcher hypothesizes that males and females differ with respect to attitude toward sports sponsorships. To investigate this hypothesis that these two groups' attitudes differ, he will use a _____.

Accepted Answer

A bivariate test of differences is most appropriate to analyze the hypothesis that males and females differ with respect to attitude toward sports sponsorships. This test will allow the researcher to compare the attitudes of both groups and determine if there is a statistically significant difference between them. Univariate tests of differences would only analyze one variable at a time and would not be appropriate for this hypothesis. Multivariate tests of differences would be useful if there were more than two groups being compared. Cluster analysis is a statistical technique used for grouping similar objects together based on their characteristics and is not suitable for testing the hypothesis in question.

Question 9

The formula given below represents the method for calculating the _____.

Accepted Answer

The answer of The formula given below represents the method...

Question 10

how do you determine the degrees of freedom in a four-cell chi-square test?

Accepted Answer

The formula for determining degrees of freedom in a four-cell chi-square test is (R-1)(C-1), where R is the number of rows and C is the number of columns. Since there are four cells, there must be two rows and two columns. Therefore, the degrees of freedom would be (2-1)(2-1), which simplifies to 1.

Question 11

In a brand awareness study, if 25 of a group of 35 males identify the brand correctly and 15 of a group of 35 females identify this brand correctly, the chi-square value for this study is approximately _____.

Accepted Answer

First, we need to create a contingency table with the data given:

|            | Males | Females | Total |
|------------|-------|---------|-------|
| Correct    | 25    | 15      | 40    |
| Incorrect  | 10    | 20      | 30    |
| **Total**  | 35    | 35      | 70    |

Next, we can calculate the expected frequencies for each cell if there were no difference between males and females in their brand awareness:

|            | Males | Females | Total |
|------------|-------|---------|-------|
| Correct    | 20    | 20      | 40    |
| Incorrect  | 15    | 15      | 30    |
| **Total**  | 35    | 35      | 70    |

To calculate the chi-square value, we use the formula:

chi-square = sum((observed - expected)^2 / expected)

Plugging in the numbers:

chi-square = ((25-20)^2/20) + ((10-15)^2/15) + ((15-20)^2/20) + ((20-15)^2/15)
chi-square = 5^2/20 + (-5)^2/15 + (-5)^2/20 + 5^2/15
chi-square = 25/20 + 25/15 + 25/20 + 25/15
chi-square = 5/4 + 5/3 + 5/4 + 5/3
chi-square = 15/4 + 10/3
chi-square = 3.75 + 3.33
chi-square ≈ 7.08

Finally, we need to compare this value to the critical chi-square value with 1 degree of freedom (df = number of rows - 1 * number of columns - 1 = 1 * 1 = 1) at the 0.05 level of significance. Using a chi-square calculator or a chi-square distribution table, the critical value is approximately 3.84.

Since our calculated chi-square value (7.08) is larger than the critical value (3.84), we can reject the null hypothesis and conclude that there is a statistically significant difference between males and females in their brand awareness. Therefore, choice C (5.84) is the best answer.

Question 12

In a study comparing the means of two groups in which there are 45 males in Group 1 and 37 females in Group 2, the degrees of freedom for this study when using the t-test for the difference between means is:

Accepted Answer

The degrees of freedom for the t-test for the difference between means is calculated as follows: df = (n1-1) + (n2-1), where n1 and n2 are the sample sizes of Group 1 and Group 2, respectively. Therefore, df = (45-1) + (37-1) = 80. Therefore, the best choice is B.

Question 13

In using the t-test to compare the means of two groups, the degrees of freedom are calculated as _____.

Accepted Answer

The degrees of freedom for an independent samples t-test are calculated as the sum of the sample sizes of the two groups, minus two (df=n1+n2-2). Therefore, the correct formula is n₁ + n₂ - 2.

Question 14

Supposed you used a 10-point rating scale to measure intention-to-buy (1 = definitely would not buy and 10 = definitely would buy). If a group of 40 males had a mean of 7 and a standard deviation of 2.5, while a group of 35 females had a mean of 5 and a standard deviation of 1.4, the standard error of the difference between the means would be approximately _____.

Accepted Answer

The answer of Supposed you used a 10-point rating scale...

Question 15

In order to use the chi-square test, the expected frequency in each of the cells of the contingency table should be at least _____.

Accepted Answer

The expected frequency in each of the cells of the contingency table should be at least 5 in order to use the chi-square test. When the expected frequency is less than 5, the test may produce unreliable results. This is known as the "rule of 5." Therefore, B is the best choice.

Question 16

Total variability is the calculated by dividing the within-group variance by the between-group variance.

Accepted Answer

Total variability is calculated by summing the within-group variance and the between-group variance. It is not obtained by dividing within-group variance by between-group variance.

Question 17

A _____ is an investigation of a hypothesis stating that two (or more) groups differ with respect to measures on a variable.

Accepted Answer

The term "test of differences" specifically refers to the investigation of a hypothesis stating that two (or more) groups differ with respect to measures on a variable. Statistical conclusions are a broad term that applies to any analysis of data, whether it involves comparing groups or not. Descriptive analysis refers to summarizing and describing data, without necessarily comparing groups. Paired comparison is a specific type of test that involves comparing two related observations, rather than two groups.

Question 18

When a researcher needs to compare means for a variable grouped into two categories based on some less-than interval variable, a(n) _____ is appropriate.

Accepted Answer

A t-test is appropriate for comparing means of a variable grouped into two categories based on some less-than interval variable. The p-test is not a standard statistical test, and the c² test and univariate test are not relevant to this context.

Question 19

All of the following are true regarding cross-tabulation EXCEPT _____.

Accepted Answer

The statement "The c² for a contingency table compares two means that are not from independent samples" is not true. Cross-tabulation is a method of analyzing the relationship between two categorical variables and comparing their frequencies to see if there is an association or correlation between them. The c² distribution and test for a contingency table is used to determine if there is a significant difference between the observed frequencies and the expected frequencies in each cell of the table.

Question 20

The total mean is the mean of a variable over all observations.

Accepted Answer

This is called the grand mean.

Quiz 22: Bivariate Statistical Analysis: Differences Between Two Variables