Exam 20: Nonparametric Tests

Exhibit 20.1.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. Refer to Exhibit 20.1.Using the critical value approach,the appropriate conclusion is:

Exhibit 20.7.A marketing firm needs to replace its existing network provider,and is considering three different providers.A primary consideration is the amount of system down time.The following table contains the amount of network down-time (in hours)for the last five months for each network provider. Refer to Exhibit 20.7.The test statistic value is:

Exhibit 20.8.A sports agent wants to understand the differences in the annual earnings of players in different sports.The below table shows the annual earnings (in million dollars)of 52 athletes.For the Kruskal-Wallis test,the rank sums for each group are at the bottom of the table. Refer to Exhibit 20.8.The p-value for the test is:

Exhibit 20.3.A company which 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. Refer to Exhibit 20.3.Using the critical value approach,appropriate conclusion is:

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

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

Exhibit 20.8.A sports agent wants to understand the differences in the annual earnings of players in different sports.The below table shows the annual earnings (in million dollars)of 52 athletes.For the Kruskal-Wallis test,the rank sums for each group are at the bottom of the table. Refer to Exhibit 20.8.For the Kruskal-Wallis test,the competing hypotheses are:

Exhibit 20.2.A trading magazine wants to determine the number of hours stock brokers 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 . Refer to Exhibit 20.2.The p-value for the test is:

Exhibit 20.11.A wine magazine wants to know if chefs can tell the difference between duck liver pate and wet dog food.Eighteen chefs were asked to rate both the pate 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. Refer to Exhibit 20.11.Assuming has the standard normal distribution,the p-value for the test is:

Exhibit 20.4.Investment institutions usually have funds with different risk vs.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 . Refer to Exhibit 20.4.Using the p-value approach and ,the appropriate conclusion is:

Parametric tests typically assume the underlying population to be normally distributed.

Exhibit 20.4.Investment institutions usually have funds with different risk vs.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 . Refer to Exhibit 20.4 Since the sample size is at least 10,T can be assumed to follow the normal distribution with mean and standard deviation:

Exhibit 20.4.Investment institutions usually have funds with different risk vs.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 . Refer to Exhibit 20.4.For the Wilcoxon signed-rank test,the competing hypotheses are:

Exhibit 20.6.A fund manager wants to know if the annual rate of return is greater for growth stocks (1)than value stocks (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. Refer to Exhibit 20.6.Using the critical value approach,the appropriate conclusion is:

Exhibit 20.10.SHY (NYSEARCA: SHY)is a 1-3 year Treasury bond fund which 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 . Refer to Exhibit 20.10.To determine if the SHY is not a market neutral position,the competing hypothesis are:

Exhibit 20.4.Investment institutions usually have funds with different risk vs.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 . Refer to Exhibit 20.4.At the 10% significance level,the critical value is:

Pearson's correlation coefficient is used as the nonparametric counterpart to the regular correlation coefficient formula.

Exhibit 20.9.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 7 packages shipped. Refer to Exhibit 20.9.The Spearman rank correlation coefficient between weight and cost is:

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

Exhibit 20.2.A trading magazine wants to determine the number of hours stock brokers 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 . Refer to Exhibit 20.2.If T is assumed to follow a normal distribution,the value of the test statistic is: