Question 1

The procedure of the Wilcoxon signed rank test is the same for either small or large sample sizes.

Accepted Answer

False

Question 2

The Mann-Whitney U test can be used to test whether two independent populations have the same median so long as the data are measured on at least an ordinal scale.

Accepted Answer

This is true. The Mann-Whitney U test is a non-parametric test used to compare whether two independent populations have the same median. It does not rely on the assumption of normality, and so can be used with data measured on at least an ordinal scale.

Question 3

In conducting the Wilcoxon signed rank test,after collecting the sample data the next step is to find the sample median and subtract this value from each data value to obtain the deviations.

Accepted Answer

In the Wilcoxon signed-rank test, the next step after collecting the sample data is to calculate the differences between the paired observations, not to find the sample median and subtract it from each data value.

Question 4

The following null and alternative hypotheses are appropriate when using a Wilcoxon signed rank test. H₀: Population Median equals 14.5 H_A_:Population Median is not equal to 14.5

Accepted Answer

The null hypothesis in a Wilcoxon signed rank test typically tests for equality of population medians (in this case, if the population median of H₀ equals 14.5). The alternative hypothesis typically tests for a difference in population medians (in this case, if the population median of _{is not equal to 14.5). Therefore, the given null and alternative hypotheses are appropriate for a Wilcoxon signed rank test.}

Question 5

If a decision maker believes that the population is normally distributed and the data are known to be ratio level,then the either the t-test or the Wilcoxon signed rank test can be used to test null hypotheses about a single population mean.

Accepted Answer

The answer of If a decision maker believes that the...

Question 6

The basic logic of the Wilcoxon signed rank test is that if about half the data values fall above the hypothesized median,and about half fall below,the null hypothesis should not be rejected.

Accepted Answer

This is the basic logic of the Wilcoxon signed rank test, so if the data follows this pattern, then the null hypothesis should not be rejected.

Question 7

Managers for a company that produces a weight loss product claim that the median weight lost over six weeks for people who use this product will be at least 20 pounds.The following data were collected from a sample of nine people who used the product.
  Based on these data,the test statistic is W = 12.

Accepted Answer

The answer of Managers for a company that produces a...

Question 8

In the Wilcoxon signed rank test for testing about a single population median,if the sample size is large (n > 20),the test statistic can be approximated by the standard normal distribution.

Accepted Answer

When the sample size is large (n > 20), the Wilcoxon signed rank test statistic can be approximated by the standard normal distribution, which makes the test more convenient and efficient to conduct.

Question 9

Recently,Major League Baseball officials stated that the median cost for a family of four to attend a baseball game including,parking,tickets,food,and drinks did not exceed $125.00.The following sample data were collected:
  Assuming that the test of the owners' claim is going to be conducted using an alpha = .05 level,the critical value is t = 1.9432.

Accepted Answer

The answer of Recently,Major League Baseball officials stated that the...

Question 10

All Wilcoxon signed rank tests are two-tailed tests since we are testing whether the population median is the exact center of the population distribution.

Accepted Answer

Wilcoxon signed rank test can also be a one-tailed test if there is a directional hypothesis (i.e., we are testing whether the population median is greater than or less than a specific value).

Question 11

Recently,Major League Baseball officials stated that the median cost for a family of four to attend a baseball game including,parking,tickets,food,and drinks did not exceed $125.00.The following sample data were collected:
  Assuming that the test of the owners' claim is going to be conducted using an alpha = .05 level,the null hypothesis that the median cost does not exceed $125 should not be rejected.

Accepted Answer

The statement in the question suggests that the null hypothesis is that the median cost (which is not the same as the mean cost) does not exceed $125. The question also states that the test will be conducted at a significance level of alpha = .05. Therefore, if the p-value of the test is greater than .05, we would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the median cost exceeds $125. Without any information about the sample data or the results of the test, we cannot say for sure whether the null hypothesis should be rejected or not. However, based on the wording of the question, we could assume that the null hypothesis is not rejected, which would lead to the answer A.

Question 12

The Wilcoxon signed rank test should be used in place of the t-test whenever the sample size is less than 20.

Accepted Answer

The Wilcoxon signed rank test and t-test are both used to compare two related samples, but the Wilcoxon signed rank test is used when the data is not normally distributed or when the sample size is small (less than 20). However, it is not a strict rule that the Wilcoxon signed rank test must be used for small sample sizes, and the decision should be based on the specific characteristics of the data being analyzed.

Question 13

Recently,Major League Baseball officials stated that the median cost for a family of four to attend a baseball game including,parking,tickets,food,and drinks did not exceed $125.00.As long as the data are considered interval or ratio level,the t-test can be used to test MLB's claim.

Accepted Answer

The answer of Recently,Major League Baseball officials stated that the...

Question 14

The Wilcoxon signed rank test is always a one-tail test with the rejection region in the upper tail.

Accepted Answer

The Wilcoxon signed rank test can be either a one-tail or a two-tail test, depending on the research hypothesis. The rejection region can be in either the upper tail, lower tail, or both tails.

Question 15

The Wilcoxon signed rank test is used for testing hypotheses about a population median if the data are at nominal level.

Accepted Answer

The Wilcoxon signed rank test is used for testing hypotheses about a population median if the data are at ordinal or interval level, not nominal level.

Question 16

The Wilcoxon signed rank test is used to test hypotheses about the population median.

Accepted Answer

The Wilcoxon signed rank test is a non-parametric test used to compare two related samples or to test hypotheses about the population median.

Question 17

In a large sample test about a single population median,it is appropriate to employ the standard normal distribution so long as the population is also normally distributed.

Accepted Answer

For a large sample test about a single population median, we use the standard normal distribution only when the sample is normally distributed, regardless of the underlying population distribution. If the sample is not normally distributed or the sample size is small, we use alternative distributions such as the t-distribution.

Question 18

In the Wilcoxon signed rank test using either small or large sample sizes,any value that equals the hypothesized median is discarded from the analysis.

Accepted Answer

In the Wilcoxon signed rank test, any value that equals the hypothesized median is assigned a rank of zero and is included in the analysis. It is not discarded.

Question 19

Managers for a company that produces a weight loss product claim that the median weight lost over six weeks for people who use this product will be at least 20 pounds.The following data were collected from a sample of nine people who used the product.
  In order to test the manager's claim,they will need to assume that the population is normally distributed.

Accepted Answer

The question does not provide any information about the population's distribution. Therefore, assuming it is normally distributed would be inappropriate.

Question 20

The Mann-Whitney U test is a nonparametric test that is used to test whether two related populations have the same median.

Accepted Answer

The Mann-Whitney U test is used to compare the medians of two independent samples, not related populations.

Quiz 17: Introduction to Nonparametric Statistics