Question 1

A t-test is not appropriate and should not be used when the sample size is greater than 30.

Accepted Answer

Researchers often employ a t-test even with large samples.As samples get larger,the t-test and Z-test will tend to yield the same results.

Question 2

A Z-test for differences of proportions requires a sample size greater than 100.

Accepted Answer

A Z-test for differences of proportions can be performed with smaller sample sizes, as long as certain assumptions are met (such as the sample proportions being approximately normally distributed). However, a larger sample size often allows for more accurate and reliable results.

Question 3

In practice, computer software is used to compute the t-test results.

Accepted Answer

Yes, computer software is commonly used to calculate t-test results. This saves time and reduces the risk of calculation errors, especially when dealing with large amounts of data. Popular software programs used for t-tests include SPSS, Excel, and R.

Question 4

One way to test the significance of contingency tables is by means of the t-test.

Accepted Answer

The t-test is not an appropriate test for contingency tables. Chi-square test is commonly used to test the significance of contingency tables.

Question 5

A pooled estimate of the standard error is a better estimate of the standard error than one based on the variance from either sample.

Accepted Answer

A pooled estimate of the standard error takes into account the variance from both samples and thus provides a more accurate estimate of the true standard error. This is why it is often used in hypothesis testing and confidence interval calculations when comparing two population means.

Question 6

The chi-square test requires that the expected frequency in each cell of the contingency table be at least 30.

Accepted Answer

The generally accepted guideline is that the expected frequency in each cell should be at least 5, not 30. However, larger expected frequencies can improve the accuracy of the test.

Question 7

The chi-square test requires the researcher to compare the observed frequencies of the groups with the expected frequencies of the groups.

Accepted Answer

The chi-square test involves comparing observed frequencies with expected frequencies to determine whether there is a significant difference between groups.

Question 8

The type of measurement, the nature of the comparison, and the number of groups to be compared influence the statistical choice.

Accepted Answer

The type of measurement, the nature of the comparison, and the number of groups to be compared are important factors that impact the statistical test that should be used. Different statistical tests have different assumptions and are appropriate for different types of data and research questions. Therefore, it is essential to carefully consider these factors when choosing a statistical test for data analysis.

Question 9

If a researcher is interested in whether males switch jobs more frequently than do females, this is an example of univariate statistics.

Accepted Answer

This is an example of bivariate statistics, as it involves the comparison of two variables (gender and job switching). Univariate statistics deals with analyzing a single variable.

Question 10

A paired-sample t-test is an appropriate test for comparing the scores of two interval variables drawn from related populations.

Accepted Answer

A paired-sample t-test is used to compare the means of two related groups, such as the scores of individuals before and after an intervention or the scores of pairs of matched individuals. This test is appropriate when the two samples are not independent and the variable of interest is measured on an interval scale. Therefore, A is the correct answer.

Question 11

Tests are bivariate tests of differences when they involve only two variables: a variable that acts like a dependent variable and a variable that acts as a classification variable.

Accepted Answer

This statement accurately describes bivariate tests.

Question 12

A cross-tabulation is a simple way to describe the relationships between two groups.

Accepted Answer

A cross-tabulation, also known as a contingency table, is a way to analyze and display the relationships and interactions between two categorical variables. It is commonly used in statistics, market research, and social sciences to understand the patterns and associations between different groups or factors.

Question 13

The t-test assumes that the two population means are equal.

Accepted Answer

The t-test does not assume that the two population means are equal. In fact, the purpose of the t-test is to determine whether there is a statistically significant difference between two population means.

Question 14

The first basic step in interpreting t-test results is to find the p-value associated with a particular t and the corresponding degrees of freedom.

Accepted Answer

This is the third step.The first step is to examine the difference in means to find the "direction" of any difference.

Question 15

The reason that means that appear to be not so close could be concluded to be statistically the same is due to the variance.

Accepted Answer

Variance measures how spread out a dataset is. If there is high variance in the data, it means that the individual data points are spread out over a wide range of values, which can result in means that appear to be not so close but are actually statistically the same.

Question 16

To use the chi-square test, both variables in a 2 x 2 contingency table must be measured on a ratio scale.

Accepted Answer

The chi-square test can be used for categorical variables, which do not necessarily have to be measured on a ratio scale.

Question 17

The degrees of freedom are calculated as d.f. = n - 1 when using the t-test for comparing two means.

Accepted Answer

In a test of two means,degrees of freedom are calculated as d.f.= n - k,where n = n₁ + n₂ and k = number of groups.

Question 18

When no direction of a relationship is stated in the hypothesis, a one-tailed test is appropriate.

Accepted Answer

When no direction of a relationship is stated in the hypothesis, a two-tailed test is appropriate because we need to consider both possibilities of the relationship being positive or negative. A one-tailed test is only appropriate when a specific direction is stated in the hypothesis.

Question 19

The t-test for comparing the means of two groups assumes that the data are in nominal scales.

Accepted Answer

The t-test assumes that the data are in interval or ratio scales. Nominal scales only allow for categorical data.

Question 20

The independent samples t-test tests the differences between means taken from two independent samples or groups.

Accepted Answer

The independent samples t-test is specifically designed to test for differences between the means of two independent groups.

Quiz 22: Bivariate Statistical Analysis: Differences Between Two Variables