Question 1

Type II error occurs when the null hypothesis is not rejected when it is false.

Accepted Answer

This is the definition of a type II error. It means that the null hypothesis should have been rejected, but was wrongly accepted.

Question 2

The purpose of hypothesis testing is not to question the computed value of the sample statistic but to make a judgment about the difference between that sample statistic and the hypothesized population parameter.

Accepted Answer

Hypothesis testing is used to determine if there is a significant difference between the sample statistic and the hypothesized population parameter, and to make a judgment on this difference based on statistical evidence. It involves formulating a null hypothesis, collecting data, and using statistical tests to determine the confidence level in rejecting or accepting the null hypothesis.

Question 3

The larger the degrees of freedom, the lower is the likelihood of observing differences among the variables.

Accepted Answer

The larger the degrees of freedom, the higher the likelihood of observing differences among the variables. This is because with more degrees of freedom, the sample size is larger, which increases the probability of finding significant differences.

Question 4

The null hypothesis associated with the sample Chi square statistic is that the two intervally scaled) variables are statistically independent.

Accepted Answer

The Chi-square test is typically used for testing relationships between categorical variables, not interval-scaled variables. The null hypothesis for a Chi-square test of independence states that there is no association between the two categorical variables.

Question 5

A p-value of .005 proves that the null hypothesis is false.

Accepted Answer

A p-value of .005 indicates that there is strong evidence against the null hypothesis, but it does not prove that the null hypothesis is false. There is always a possibility of a Type I error (rejecting the null hypothesis when it is actually true).

Question 6

The number of degrees of freedom, v, for the chi‐square test of independence is obtained using the formula v = r -1) * c -1).

Accepted Answer

This formula is correct and is used to determine the number of degrees of freedom for the chi-square test of independence, where r is the number of rows and c is the number of columns in the contingency table.

Question 7

The process of hypothesis testing, begins with an assumption about a sample statistic

Accepted Answer

Hypothesis testing begins with an assumption about a population parameter, not a sample statistic.

Question 8

A p-value of .45 means that the evidence against the null hypothesis is very weak.

Accepted Answer

A p-value of .45 indicates that there is a high probability of obtaining the observed results under the assumption of the null hypothesis. This suggests that there is not enough evidence to reject the null hypothesis and support the alternative hypothesis. Therefore, the evidence against the null hypothesis is weak.

Question 9

Assuming the hypothesis to be true, the significance level indicates the percentage of sample means that are outside the cutoff limits.

Accepted Answer

The significance level (alpha level) represents the probability of rejecting the null hypothesis when it is actually true. It is not related to the percentage of sample means outside the cutoff limits. The cutoff limits are determined by the level of significance and the sample size.

Question 10

If the p-value is less than or equal to 0.05, then it is valid to say that the sample evidence is significant at .05 level.

Accepted Answer

The rule of thumb is that if the p-value is less than or equal to the significance level (usually set at 0.05), then the results are considered statistically significant. Therefore, it is valid to say that the sample evidence is significant at the 0.05 level if the p-value is less than or equal to 0.05.

Question 11

A high p-value means that the probability of a statistically significant difference is high.

Accepted Answer

A high p-value actually means that there is a high probability that any observed difference between groups occurred by chance and is not statistically significant. A small p-value (typically less than 0.05) indicates strong evidence against the null hypothesis and suggests that the observed difference is likely not due to chance.

Question 12

Two branches of a major multinational corporation conducted surveys to measure the association between income level low, mid, high) and need for a certain produce low, mid, high).The sample size in one survey was 100 and in the other, 200.The branches now wish to compare the two cross tabulations that were generated from the surveys.Given this information, the Chi square statistic would provide an easy-to-interpret method to compare the associations.

Accepted Answer

The answer of Two branches of a major multinational corporation...

Question 13

A high value of b indicates that the test of hypothesis is working very well.

Accepted Answer

A high value of b indicates that the test of hypothesis is not working well, as it means that the probability of rejecting a false null hypothesis is low.

Question 14

The hypothesis test serves to quantify the reliability of research results, indicating the extent to which the data support the empirical findings.

Accepted Answer

This is an accurate description of the purpose and function of a hypothesis test in research.

Question 15

The higher the significance level used for testing a hypothesis, the higher is the probability of rejecting the null hypothesis when it is true.

Accepted Answer

This is because a higher significance level means we are willing to tolerate a higher chance of making a Type I error (rejecting the null hypothesis when it is actually true), which increases the likelihood of rejecting the null hypothesis.

Question 16

Degrees of freedom refers to the number or bits of "free" or unconstrained data used in calculating a sample statistic.

Accepted Answer

This is an accurate definition of degrees of freedom.

Question 17

A major advantage of the Chi square statistic as a measurement of association between two questions is that it is independent of the sample size, making it easy to interpret in an absolute sense.

Accepted Answer

The statement is incorrect. Chi square statistic is influenced by sample size, so comparing chi-square values between studies with different sample sizes may not be appropriate.

Question 18

The contingency coefficient varies between 0 and 1.The 0 value occurs in the case of no association i.e., the variables are statistically independent), but the maximum value of 1 is never achieved.

Accepted Answer

This statement is true. The contingency coefficient, also known as Cramer's V coefficient, ranges from 0 to 1. A value of 0 indicates no association or independence between two variables, while the maximum value of 1 is not achievable due to mathematical limitations.

Question 19

The Chi square test can provide a useful measurement of association.

Accepted Answer

The Chi square test is a statistical test that can be used to determine if there is a significant association between two variables. It is widely used in the field of social sciences and can be used to test hypotheses about the relationship between categorical variables. Therefore, it can provide a useful measurement of association.

Question 20

In order to reduce the probability of committing a Type II error, the probability of committing a Type I error must necessarily decreased

Accepted Answer

Reducing the probability of committing a Type II error (increasing power) does not necessarily require decreasing the probability of committing a Type I error. Adjustments to sample size, effect size, or significance level can independently affect these errors.

Quiz 17: Hypothesis Testing: Basic Concepts and Tests of Association