Question 1

The alternative hypothesis is a statement that some difference or effect is expected.

Accepted Answer

The alternative hypothesis is usually formulated as a statement of some expected difference or effect, while the null hypothesis assumes no difference or effect.

Question 2

In commercial marketing research, the one-tailed test is used more often than a two-tailed test.

Accepted Answer

The one-tailed test is commonly used in commercial marketing research because it is designed to test a specific hypothesis in a particular direction, which is often the focus of the research question. The two-tailed test is less common because it tests for a difference in both directions, which may not be as relevant or necessary for the research question at hand.

Question 3

Cross-tabulation examines associations between variables, not causation.

Accepted Answer

Cross-tabulation is a descriptive statistical method that helps examine the relationship between two or more categorical variables. It does not establish causation between the variables, but only identifies potential associations.

Question 4

If the calculated value of the test statistic is less than the critical value of the test statistic (TS _CR), the null hypothesis is rejected.

Accepted Answer

If the calculated value of the test statistic is less than the critical value of the test statistic, it means we fail to reject the null hypothesis. The null hypothesis is only rejected if the calculated value of the test statistic is greater than the critical value.

Question 5

The test statistic measures how close the sample has come to the null hypothesis and often follows a well-known distribution, such as the normal, t, or chi-square distribution.

Accepted Answer

This is a true statement. The test statistic quantifies the difference between the observed data and the expected results under the null hypothesis. It is then compared to the distribution of the test statistic under the null hypothesis and a p-value is calculated to determine the statistical significance of the results. Commonly used distributions for test statistics include the normal, t, and chi-square distributions.

Question 6

The first step in hypothesis testing is to select an appropriate statistical technique and the corresponding test statistic.

Accepted Answer

The first step in hypothesis testing is to state the null and alternative hypotheses.

Question 7

A cross-tabulation is the merging of the frequency distribution of two or more variables in a single table to help us to understand how one variable relates to another variable.

Accepted Answer

This statement is true. A cross-tabulation (also known as a contingency table) displays the distribution of one variable in relation to another variable and can show patterns and relationships between the two variables.

Question 8

If the probability associated with the calculated or observed value of the test statistic (TS _CAL)is greater than the level of significance (α), the null hypothesis is rejected.

Accepted Answer

If the probability associated with the calculated or observed value of the test statistic is greater than the level of significance (α), the null hypothesis is not rejected. The null hypothesis is rejected only when this probability is less than or equal to the level of significance.

Question 9

Type I error occurs when the sample results lead to the rejection of the null hypothesis when it is in fact true.

Accepted Answer

This is the definition of Type I error, also known as a false positive.

Question 10

The probability of Type II error (α)is also called the level of significance.

Accepted Answer

The probability of Type II error is not the same as the level of significance (α), but rather it is denoted by β. The level of significance (α) is the maximum probability of making a Type I error, which is rejecting a true null hypothesis.

Question 11

In cross-tabulation, the introduction of a third variable clarifies the initial association (or lack of it)observed between two variables and can result in six possibilities.

Accepted Answer

The answer of In cross-tabulation, the introduction of a third...

Question 12

The two-tailed test is more powerful than the one-tailed test.

Accepted Answer

A two-tailed test is not inherently more powerful than a one-tailed test; it is used when the direction of the effect is not specified, thus requiring more evidence to reject the null hypothesis for a given significance level compared to a one-tailed test, which focuses on a specific direction.

Question 13

For a given level of α, increasing the sample size will decrease β, thereby increasing the power of the test.

Accepted Answer

This statement is true. As the sample size increases, the standard error decreases and the distribution of the test statistic becomes narrower, reducing the potential for a Type II error (i.e., β decreases) and increasing the power of the test.

Question 14

In tests of associations, the null hypothesis is that there is no association between the variables (H₀:......is NOT related to....).

Accepted Answer

The null hypothesis in tests of associations is that there is no association between the variables being tested.

Question 15

In tests of differences, the null hypothesis is that there is a difference (H₀:.....is different than....).

Accepted Answer

The null hypothesis in tests of differences is that there is no difference between the compared groups or variables. Therefore, the statement "H₀:.....is different than...." would be the alternative hypothesis, not the null hypothesis.

Question 16

In determining the critical value of the test statistic, the area to the right of the critical value is either α or α/2.It is α for a one-tail test and α/2 for a two-tail test.

Accepted Answer

This statement is true. For a one-tail test, we are only interested in extreme values in one direction, so we only need to consider the area in that one tail. Therefore, the area to the right of the critical value is the significance level (α). For a two-tail test, we are interested in extreme values in either direction, so we need to consider the area in both tails. In this case, we split the significance level (α) evenly between the two tails, so each tail has an area of α/2.

Question 17

The null hypothesis is always the hypothesis that is tested.

Accepted Answer

The null hypothesis is the hypothesis that is tested in a statistical analysis, as it represents the hypothesis that there is no effect or no difference, and the aim is to either reject it or fail to reject it based on the data.

Question 18

When using the chi-square statistic in cross-tabulation, the null hypothesis (H₀)will be rejected only when the calculated value of the test statistic is greater than the critical value of the chi-square distribution with the appropriate degrees of freedom.

Accepted Answer

This statement is true. The chi-square test compares the observed frequencies in a cross-tabulation with the expected frequencies under the null hypothesis. If the calculated value of the test statistic is larger than the critical value of the chi-square distribution with the appropriate degrees of freedom (typically with a significance level of 0.05 or 0.01), then the null hypothesis is rejected and it is concluded that there is a significant association between the two variables in the cross-tabulation.

Question 19

The null hypothesis, H₀, when using the chi-square statistic, is that there is no association between the variables.

Accepted Answer

The null hypothesis for chi-square test is that there is no association between the two variables being tested. Therefore, H₀ statement indicates a null hypothesis of no association.

Question 20

The null hypothesis refers to a specified value of the population parameter, not a sample statistic.

Accepted Answer

The null hypothesis is always related to the population parameter, not a sample statistic. The null hypothesis assumes that there is no significant difference between two groups or variables. It is the opposite of the alternative hypothesis, which assumes that there is a significant difference between two groups or variables.

Quiz 15: Frequency Distribution, Cross-Tabulation, and Hypothesis Testing