Exam 20: Nonparametric Tests

A real estate agent wants to know how the home size (in square feet) of parents compares to the home size of their children. For a sample of seven parents and their children, the value of the test statistic for the Wilcoxon signed-rank test for a matched pairs sample is T = T⁺ = 27. The differences are calculated as the parent's home size subtracted by the child's home size. A) Specify the competing hypothesis to determine if the median difference in home size between parents and children is greater than zero. B) At the 5% significance level, what is the critical value? C) At the 5% significance level, what is the decision and conclusion?

For the Spearman rank correlation test we can use the normal distribution approximation to implement a z test only if n is greater or equal to ________.

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. The p-value for the test 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. Using the critical value approach and α = 0.05, the appropriate conclusion is ________.

Which of the following is the test statistic for the Kruskal-Wallis test?

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. Using the critical value approach and α = 0.01, the appropriate conclusion is ________.

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. Which of the following are the competing hypotheses to determine if the median number of hours worked per week differs from 100 hours?

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 test statistic value 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. For the Kruskal-Wallis test, 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 critical 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. To determine whether the medians of the taxes paid differ using the Wilcoxon rank-sum test, the competing hypotheses are ________.

A university advisor wants to determine if there is a difference in the total amount of time spent studying between students taking an online version and a traditional class version of a certain course. The following table contains the sample sizes of each group, and the rank sums for the Wilcoxon rank-sum test. a. Specify the competing hypothesis to determine whether the median study time for online students differs from the median study time for traditional students. B) What is the value of the Wilcoxon rank-sum test statistic W? C) Assuming W follows a normal distribution, what is the value of the corresponding test statistic? D) At the 1% significance level, what is the decision and conclusion?

If the distributional assumptions of a parametric test are valid yet we choose to use a nonparametric test, the nonparametric test is more powerful.

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. Using the p-value approach and α = 0.01, the appropriate conclusion is ________.

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 p-value approach and α = 0.01, the appropriate conclusion is ________.

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. The p-value for the test is ________.

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. Using the p-value approach and α = 0.05, the appropriate conclusion is ________.

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. Because both sample sizes are at least 10, the sampling distribution of W can be approximated by the normal distribution with a mean and standard deviation of ________, respectively.

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 mean of ________.

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. Using the critical value approach and α = 0.10, the appropriate conclusion is ________.