Exam 20: Nonparametric Tests

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.Using the p-value approach and ,the appropriate conclusion is:

A study was conducted to determine if husbands and wives like the same TV shows.Married couples ranked 15 TV shows,and the Spearman rank correlation coefficient was found to be . A)Specify the competing hypotheses to determine if there is a positive correlation between the two rankings. B)Assuming the Spearman rank correlation coefficient follows a normal distribution,what are the mean and standard deviation of the normal distribution? C)Assuming the Spearman rank correlation coefficient follows a normal distribution,what is the value of the test statistic? D)At the 5% significance level,what is the decision and conclusion?

The nonparametric test for ordinal data under matched-pairs sampling 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.Using the p-value approach and ,the appropriate conclusion is:

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.At the 10% significance level,the positive critical value is:

Parametric tests are distribution-free tests.

Exhibit 20.5.An accountant wants to know if the property taxes paid by clients that live in the city are different from those that live in the county.The property taxes paid by five clients from the city (1)and five clients from the county (2)are shown below (in dollars). Refer to Exhibit 20.5.At the 5% significance level,the critical values are:

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.For the Kruskal-Wallis test,the competing hypotheses are:

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

Exhibit 20.5.An accountant wants to know if the property taxes paid by clients that live in the city are different from those that live in the county.The property taxes paid by five clients from the city (1)and five clients from the county (2)are shown below (in dollars). Refer to Exhibit 20.5.Using the critical value approach,the appropriate conclusion is:

Exhibit 20.5.An accountant wants to know if the property taxes paid by clients that live in the city are different from those that live in the county.The property taxes paid by five clients from the city (1)and five clients from the county (2)are shown below (in dollars). Refer to Exhibit 20.5.The value of the test statistic is:

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.To determine if the weights and costs are significantly correlated,the competing hypothesis 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.Using the p-value approach and ,the appropriate conclusion 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 critical value approach,appropriate conclusion 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 value of the test statistic for the sign 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.Specify the competing hypotheses to determine if the median sale price is greater than $150.

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.Since the sample size is greater than 10 and can be assumed to follow a normal distribution,the value of the test statistic is

For n_i ≥ 5,the test statistic,H,for the Kruskal-Wallis test is assumed to follow:

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.Since the number of heads and tails are larger than ten,the test statistic R can be assumed to follow a normal distribution.The value of the test statistic is:

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.Since both sample sizes are at least 10,W can be assumed to follow a normal distribution with a mean and standard deviation of: