Exam 20: Nonparametric Tests

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

The sign test on a matched-pairs sample is similar to the Wilcoxon signed-rank test but applied to ordinal data.

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.Since the sample size is at least 10,T can be assumed normally distributed with mean and standard deviation:

The null hypothesis of the Wald-Wolfowitz runs test is the elements do not occur randomly.

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.To determine if there are differences in preferences between pate and dog food using the sign 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.To determine whether the median return of growth funds is larger than the median return of value funds,the competing hypotheses are:

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.For the Wilcoxon signed-rank test,the competing hypotheses 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.The p-value for the test is:

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.The p-value for the test is:

A trading magazine wants to know if a seminar on self-confidence helps stockbrokers to obtain new clients.Before and after the self-confidence seminar,14 stockbrokers rated their self-confidence as low,neutral,or high.In comparing the before and after rankings,there was one plus sign and 13 negative signs for the sign test. A)Specify the competing hypotheses to determine if there are differences in self-confidence before and after the seminar. B)Assuming the proportion of plus signs follows a normal distribution,what is the value of the test statistic? C)At the 1% significance level,what is the decision and conclusion?

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.The p-value for the test is:

For the Wilcoxon signed-rank test with n ≥ 10,the test statistic is assumed to follow a normal distribution with mean:

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?

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.Assuming that W follows a normal distribution,the value of the test statistic is

Exhibit 20.12.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. Refer to Exhibit 20.12.For the Wald-Wolfowitz runs test,the value of R 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.At the 1% significance level,the critical value is

The test statistic for the sign test is ,where:

For the Wilcoxon rank-sum test with the sample sizes being at least 10,the test statistic can be assumed to follow a normal distribution with mean:

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.The p-value for the test is:

Exhibit 20.13.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,6 runs are below the median,and 5 runs are above the median. Since Refer to Exhibit 20.13.Assume the test statistic R follows a normal distribution.The value of the test statistic is: