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 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.Assuming that T follows a normal distribution,the value of the test statistic 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.To determine if the coin is fair using the Wald-Wolfowitz runs test,the competing hypotheses are _________.

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 _______________________________________________.

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 _________.

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 ber_s = -0.284.The p-value for the test is ______________.

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 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?

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 ______________________________________.