Exam 20: Nonparametric Tests

The Kruskal-Wallis test is the nonparametric alternative to one-way ANOVA.

Which of the following is the sample Spearman rank correlation coefficient?

A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median numbers worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T⁺ = 153. Given the sample size, the sampling distribution of T can be approximated by the normal distribution with mean and standard deviation ________, respectively.

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. To determine whether chefs have a preference between pâté and dog food using the sign test, the competing hypotheses are ________.

A trading magazine wants to determine the number of hours stockbrokers work each week. In particular, the trading magazine wants to determine if the median number of hours worked per week differs from 100 hours. The magazine samples 18 traders. For the Wilcoxon signed-rank test, the value of the test statistic is T = T⁺ = 153. The p-value for the test is ________.

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. Assuming the sampling distribution of R can be approximated by the normal distribution, the p-value for the test is ________.

The nonparametric test for two population medians under independent sampling is known as ________.

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds is 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. Using the p-value approach and α = 0.10, 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. For the Kruskal-Wallis test, the competing hypotheses are ________.

SHY (NYSEARCA: SHY) is a 1-3-year Treasury bond fund that is considered to be a market-neutral position. Using the S&P 500 as a benchmark and five years of monthly log-return data, the rank correlation coefficient of SHY with the S&P 500 is found to be r_s = -0.284. To determine if the SHY is not a market-neutral position, the competing hypotheses are ________.

A company that produces financial accounting software wants to offer better training to its customers. The training is intended to decrease the amount of time required to do complicated accounting calculations. For seven individuals, the amount of time (in minutes) to complete a complicated calculation is determined before and after completing the new training. Using the p-value approach and α = 0.05, the appropriate conclusion is ________.

An accountant wants to know if the property taxes paid by clients who live in the city are different from those who live in the county. The property taxes paid by five clients from the city (sample 1) and five clients from the county (sample 2) are shown below. The value of the test statistic is ________.

A sports agent wants to understand the differences in the annual earnings of players in different sports. The following table shows the annual earnings (in million $) of 52 athletes. For the Kruskal-Wallis test, the rank sums for each group are at the bottom of the table. The p-value for the test is ________.

The Kruskal-Wallis test is always a ________-tailed test.

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. The p-value for the test is ________.

For the Wald-Wolfowitz runs test with n₁ ≥ 10 and n₂ ≥ 10, the sampling distribution of the test statistic R can be approximated by the normal distribution with standard deviation ________.

Which of the following is the test statistic for the sign test?

A magician has a coin that may or may not be fair. The results of 30 flips of the coin are H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T.Since the number of heads and tails are larger than 10, the sampling distribution of the test statistic R can be approximated by the normal distribution. The value of the test statistic is ________.

The Wilcoxon rank-sum test is used as a nonparametric counterpart to the matched-pairs t test.

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. To determine whether the median return of growth funds is larger than the median return of value funds, the competing hypotheses are ________.