Exam 20: Nonparametric Tests

An energy analyst wants to test if U.S. oil production is random over time. The analyst has monthly production values for the two years. The analyst finds 12 months are above the median, 12 months are below the median, six runs are below the median, and five runs are above the median. Assume the R follows a normal distribution. The value of the test statistic is ________.

A research analyst believes that a positive relationship exists between a firm's advertising expenditures and its sales. For 65 firms, she collects data on each firm's yearly advertising expenditures and its sales. She calculates a Spearman rank correlation coefficient of 0.45. The value of the test statistic and p-value are ________, respectively.

For the Wilcoxon signed-rank test with n ≥ 10, the sampling distribution of the test statistic can be approximated by the normal distribution with mean ________.

For the Wilcoxon rank-sum test when the sample sizes are at least 10, the sampling distribution of the test statistic can be approximated by the normal distribution with standard deviation ________.

An energy analyst wants to test if U.S. oil production is random over time. The analyst has monthly production values for the two years. The analyst finds 12 months are above the median, 12 months are below the median, six runs are below the median, and five runs are above the median. For the Wald-Wolfowitz runs test, the value of R is ________.

A career counselor is comparing the annual salary of executives in the manufacturing, finance, and engineering industries. The following table shows the sample size for each industry and the rank sum for the Kruskal-Wallis test. a. Specify the competing hypotheses to determine whether differences exist in the median annual salary of the three industries. B) What is the value of the Kruskal-Wallis test statistic H? C) At the 5% significance level, what is the decision and conclusion?

A research analyst believes that a positive relationship exists between a firm's advertising expenditures and its sales. For 65 firms, she collects data on each firm's yearly advertising expenditures and its sales. She calculates a Spearman rank correlation coefficient of 0.45. Which of the following are the competing hypotheses to determine whether the Spearman rank correlation coefficient differs from the zero?

The method of runs above and below the median is especially useful in detecting trends and cyclical patterns in ________ data.

A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test. Using the critical value approach and α = 0.01, the appropriate conclusion is ________.

A shipping company believes there is a linear association between the weight of packages shipped and the cost. The following table shows the weight (in pounds) and cost (in dollars) of the last seven packages shipped. The Spearman rank correlation coefficient between weight and cost is ________.

A trading magazine wants to know if a seminar on self-confidence helps stockbrokers to obtain new clients. Before and after the self-confidence seminar, 14 stockbrokers rated their self-confidence as low, neutral, or high. In comparing the before and after rankings, there was one plus sign and 13 negative signs for the sign test. A) Specify the competing hypotheses to determine if there are differences in self-confidence before and after the seminar. B) Assuming the proportion of plus signs follows a normal distribution, what is the value of the test statistic? C) At the 1% significance level, what is the decision and conclusion?

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds are greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return − low-risk return, the value of the test statistic is T = T⁺ = 185. Given the sample size, the sampling distribution of T can be approximated by the normal distribution as the sample size is greater than 10; T can be assumed to follow the normal distribution with mean and standard deviation ________, respectively.

A pawn shop claims to sell used Kindles for about the same price as Amazon or eBay. Both online retailers sell used Kindles for around $150. Below are recent Kindle sales prices for the pawn shop. Using the p-value approach and α = 0.05, the appropriate conclusion is ________.

When conducting a hypothesis test for the ________ m, we want to determine whether m is not equal to, greater than, or less than m₀, the value of the population median postulated in the null hypothesis.

A wine magazine wants to know if chefs can tell the difference between duck liver pâté and wet dog food. Eighteen chefs were asked to rate both the pâté and dog food on a scale from 1 to 5, with 1 corresponding to "inedible" and 5 to "very tasty." The results are shown in the following table. Assuming the sampling distribution of can be approximated by the standard normal distribution, the p-value for the test is ________.

A pawn shop claims to sell used Kindles for about the same price as Amazon or eBay. Both online retailers sell used Kindles for around $150. Below are recent Kindle sales prices for the pawn shop. Using the critical value approach and α = 0.05, the appropriate conclusion is ________.

A marketing firm needs to replace its existing network provider and is considering three different providers. A primary consideration is the amount of system downtime. The following table contains the amount of network downtime (in hours) for the last five months for each network provider. At the 5% significance level, the critical value is ________.

The Wilcoxon signed-rank test for a population median does not assume anything about the distribution of the population.

The Wilcoxon rank-sum test is based completely on the ________ of the observations from the two independent samples.

The null hypothesis of the Wald-Wolfowitz runs test is the elements do not occur randomly.