Question 1

The number on baseball players' uniforms is an example of nominal data.

Accepted Answer

The numbers on baseball players' uniforms are used to identify different players, not to rank or quantify them, which is characteristic of nominal data.

Question 2

The null hypothesis for the Kruskal- Wallis test always states that there is no difference among the means of the populations being tested.

Accepted Answer

The Kruskal-Wallis test is a non-parametric test that compares the medians from three or more independent samples to determine if they come from the same distribution. It does not specifically test differences among means.

Question 3

The test statistic for the one- tail sign test, S, is the number of plus signs regardless of the type of alternative hypothesis.

Accepted Answer

The test statistic for the one-tail sign test, S, depends on the type of alternative hypothesis (whether it's testing for an increase or a decrease), so it could be the number of plus signs or minus signs, not just the plus signs.

Question 4

The sign test is a nonparametric procedure that assigns a plus sign or a minus sign to each observation in a sample.

Accepted Answer

The sign test is indeed a nonparametric procedure used to test the median of a population or compare the medians of two dependent samples. It involves assigning a plus sign (+) to observations above the median and a minus sign (-) to those below the median, ignoring any observations that are equal to the median.

Question 5

The sign test can be used to determine if consumers prefer one product or service over another.

Accepted Answer

The sign test is a non-parametric test used to evaluate whether there is a statistically significant difference between two related samples, such as consumer preferences for two products or services, based on the direction of changes or differences between pairs without assuming a specific distribution for these differences.

Question 6

Parametric statistics require the level of data measurement to be ordinal or interval.

Accepted Answer

Parametric statistics typically require interval or ratio level of measurement because they assume the underlying data distributions are normal, and these levels of measurement support the arithmetic operations and assumptions necessary for parametric tests. Ordinal data, which merely ranks items without implying equal distances between ranks, generally does not meet the requirements for parametric statistical tests.

Question 7

Parametric statistics are procedures that rely on fewer assumptions about the probability distribution for a population of interest than nonparametric statistics do.

Accepted Answer

Parametric statistics rely on more assumptions about the probability distribution for a population of interest, such as normality, than nonparametric statistics, which require fewer assumptions about the population's distribution.

Question 8

Ordinal data has all of the properties of interval data with the added feature that allows us to measure the differences between the categories with actual numbers in a meaningful way.

Accepted Answer

Ordinal data allows for ranking and order but does not specify the exact difference between the categories, unlike interval data which does quantify the differences between points.

Question 9

Nominal data has all the properties of interval data with the added benefit of having a true zero point.

Accepted Answer

Nominal data is categorical and does not imply any order or numerical difference between categories, unlike interval data which indicates both order and the exact differences between values but lacks a true zero point.

Question 10

If the test statistic for the Kruskal- Wallis test is greater than the critical value for the Kruskal- Wallis test, the null hypothesis is rejected.

Accepted Answer

When the test statistic for the Kruskal-Wallis test exceeds the critical value, it indicates that there is a statistically significant difference among the groups, leading to the rejection of the null hypothesis.

Question 11

The Wilcoxon rank- sum test is a nonparametric procedure that determines whether two populations have the same probability distribution based on evidence from two independent samples.

Accepted Answer

The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is indeed a nonparametric statistical test used to compare two independent samples to assess whether their underlying population distributions differ significantly. It does not assume the data to be normally distributed and is used as an alternative to the t-test when the data do not meet the t-test assumptions.

Question 12

The sign test can be used to perform a hypothesis test for a population mean.

Accepted Answer

The sign test is a non-parametric test used to evaluate the median of a population rather than the mean. It is typically used when the assumptions for parametric tests are not met.

Question 13

The Spearman rank- order correlation coefficient is a nonparametric procedure measures the strength and direction of the relationship between two variables.

Accepted Answer

The Spearman rank-order correlation coefficient is indeed a nonparametric measure that assesses the strength and direction of association between two ranked variables.

Question 14

Because each observation from a sample for the sign test must be assigned a plus or minus sign, this sampling distribution can be said to follow the binomial probability distribution.

Accepted Answer

The sign test assigns a plus or minus sign to each observation based on whether it is above or below a median value, and since each observation has only two outcomes (positive or negative), the sampling distribution of the number of positive or negative signs follows a binomial probability distribution.

Question 15

Interval data has all of the properties of ordinal data with the added feature that allows us to measure the differences between the categories with actual numbers in a meaningful way.

Accepted Answer

Interval data includes the properties of ordinal data (i.e., data can be ordered), and also allows for the calculation of meaningful differences between data points, but does not have a true zero point, unlike ratio data.

Question 16

All else being equal (the same sample size, same level of significance, and so on), the parametric procedure will result in a higher probability of your correctly rejecting the null hypothesis.

Accepted Answer

Parametric tests are generally more powerful than non-parametric tests when their assumptions are met, meaning they have a higher probability of detecting a true effect (correctly rejecting the null hypothesis) when it exists.

Question 17

The smaller the test statistic for the Wilcoxon signed- rank test, the more likely that we will be able to reject the null hypothesis.

Accepted Answer

In the Wilcoxon signed-rank test, a smaller test statistic indicates a greater deviation from the null hypothesis, suggesting that the observed differences are not due to random chance, thus increasing the likelihood of rejecting the null hypothesis.

Question 18

The Wilcoxon rank- sum test requires the data be at least at the ordinal level of measurement and that the shapes of the distributions for the two populations are similar.

Accepted Answer

The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, requires that the data be at least ordinal because it ranks the observations. Additionally, for the test to be most effective, it assumes that the distributions of the two populations are similar in shape, though it does not require them to follow a normal distribution.

Question 19

The large sample case of the Wilcoxon rank- sum test (n1 > 10 and n2 > 10), the test statistic can be approximated by the binomial probability distribution.

Accepted Answer

The large sample case of the Wilcoxon rank-sum test statistic is approximated by a normal distribution, not a binomial probability distribution.

Question 20

The Spearman rank- order correlation coefficient requires the data be at the nominal level of measurement.

Accepted Answer

The Spearman rank-order correlation coefficient requires the data to be at least at the ordinal level of measurement, not nominal.

Quiz 16: Forecasting Techniques and Analysis for Time Series Data