Exam 20: Nonparametric Tests

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. At the 10% significance level, the critical value is ________.

A magician has a coin that may or 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. At the 10% significance level, the critical value for the test is ________.

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. Using the critical value approach, appropriate conclusion 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. The estimate of the population proportion of plus signs is ________.

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. Given the sample size, the sampling distribution of r_s can be approximated by the normal distribution and the value of the test statistic is ________.

The test statistic for the sign test is = where ________.

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. For the Wald-Wolfowitz runs test, the value of the total number of runs R is ________.

The nonparametric test for the correlation between two variables is known as the ________.

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. At the 10% significance level, the positive critical value 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 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. Using the p-value approach and α = 0.01, the appropriate conclusion is ________.

The nonparametric test for a single population median is known as the ________.

Let positive daily S&P 500 returns define up days, and negative daily S&P 500 returns define down days. A stockbroker wants to know if the up and down days of the S&P 500 occur randomly. For 30 trading days, there were 17 up days, 13 down days, four runs of up days, and four runs of down days. A) Specify the competing hypotheses to determine whether the S&P 500 up and down days occur at random. B) What is the value of the Wald-Wolfowitz runs test statistic? C) At the 5% significance level, what is the decision and conclusion?

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. 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. Which of the following is the value of the test statistic?

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

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. At the 5% significance level, the critical value 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. Assuming that the sampling distribution of W can be approximated by the 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. At the 5% confidence level, which of the following is the correct conclusion about the relationship between advertising and sales?

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