Question 1

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 2

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 Chi square statistic is not independent of sample size and its interpretation depends on the sample size.

Question 3

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

Accepted Answer

Degrees of freedom are the number of unconstrained data points used in calculating a sample statistic.

Question 4

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

A p-value less than or equal to 0.05 indicates that there is less than a 5% chance of observing the data if the null hypothesis is true. Therefore, the evidence supports rejecting the null hypothesis and accepting the alternative hypothesis, making the results statistically significant at the .05 level.

Question 5

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 a lower threshold for accepting evidence against the null hypothesis, which increases the likelihood of a false positive or Type I error (rejecting the null hypothesis when it is actually true).

Question 6

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

Accepted Answer

Type II error is the failure to reject a false null hypothesis.

Question 7

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

Accepted Answer

A p-value of .005 only indicates that the observed data is unlikely to have occurred by chance if the null hypothesis were true. It does not prove that the null hypothesis is false. It simply suggests that we reject the null hypothesis in favor of an alternative hypothesis.

Question 8

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 the observed effect is due to chance and not a true difference between groups. A low p-value (typically less than 0.05) indicates that the observed effect is unlikely to be due to chance and there is a statistically significant difference between groups.

Question 9

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 is the likelihood of observing differences among the variables. This is because larger degrees of freedom indicate a larger sample size and therefore, a greater ability to detect small differences or deviations from expected values.

Question 10

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 45% chance that the observed results could have occurred by chance alone, assuming the null hypothesis is true. This is considered weak evidence against the null hypothesis, as it is a relatively high probability of obtaining such results by chance. Therefore, the statement is true.

Question 11

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

Accepted Answer

The hypothesis test is used to determine the statistical significance of the research results and to evaluate the likelihood that the findings are due to chance or random variation. It helps to quantify the reliability and validity of the research data by indicating the extent to which they support the hypothesis or research question being tested.

Question 12

If an analyst computes "marginal," he or she simply computes frequency distributions for the individual questions.

Accepted Answer

Marginal analysis involves examining the frequency distribution of individual variables without considering their relationship with other variables.

Question 13

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 14

The confidence with which we may reject/accept a hypothesis is independent of the sample size, but dependent on the true population variance.

Accepted Answer

The confidence with which we may reject/accept a hypothesis is dependent on both the sample size and the true population variance. As sample size increases, the standard error decreases and the confidence in the results increases. Additionally, if the population variance is larger, it may be more difficult to reject or accept a hypothesis with a high degree of confidence.

Question 15

If the sample size increases, the p-value will usually become smaller.

Accepted Answer

As the sample size increases, there is more evidence to support the hypothesis being tested, which usually results in a smaller p-value.

Question 16

After analyzing repeat purchase sales data from two market segments, the researcher reported that the p-value was 0.15.This implies that there are more than 15 chances out of 100 that the difference found was simply due to a sampling accident.

Accepted Answer

The answer of After analyzing repeat purchase sales data from...

Question 17

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 alternative hypothesis is more likely to be true than the null hypothesis, but it does not necessarily mean that the test of hypothesis is working very well. The overall performance of the test also depends on other factors such as sample size and significance level.

Question 18

A p-value of .07 means that the results are statistically significant at the 0.05 level. Assume that a new product is placed in a sample of stores.The sample mean for units sold is 35 units.We test the hypothesis that the population mean is only 20.

Accepted Answer

A p-value of .07 means that there is a 7% chance of obtaining a sample mean of 35 units or more, assuming the population mean is actually 20. This is not considered statistically significant at the 0.05 level since the p-value is greater than 0.05. Therefore, we cannot reject the hypothesis that the population mean is 20 based on this test result.

Question 19

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

Accepted Answer

The Chi square test is commonly used to measure the association between two categorical variables, making it a useful tool for statistical analysis.

Question 20

We can be more confident in rejecting the null hypothesis with a p-value of 0.05 than with a p-value of 0.02.

Accepted Answer

A p-value of 0.02 indicates stronger evidence against the null hypothesis than a p-value of 0.05, making us more confident in rejecting the null hypothesis with the lower p-value.

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