Exam 20: Nonparametric Tests

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.Which of the following are the competing hypotheses to determine whether the Spearman rank correlation coefficient differs from the zero?

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

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.Using the p-value approach and α = 0.10,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. Using the p-value approach and α = 0.05,the 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. To determine if there are differences in preferences between pâté and dog food using the sign 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. At the 5% significance level,the critical value is ____.

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?

A marketing firm needs to replace its existing network provider and is considering three different providers.A primary consideration is the amount of system downtime.The following table contains the amount of network downtime (in hours)for the last five months for each network provider. The test statistic value 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.Because the sample size is greater than 10 and r_s can be assumed to follow a normal distribution,the value of the test statistic is ________.

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

Parametric tests are distribution-free tests.

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. Assuming has the standard normal distribution,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?

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

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

A marketing firm needs to replace its existing network provider and is considering three different providers.A primary consideration is the amount of system downtime.The following table contains the amount of network downtime (in hours)for the last five months for each network provider. For the Kruskal-Wallis test,the competing hypotheses are ___________.

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.For the Wald-Wolfowitz runs test,the value of R is ____.

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

The sign test is used to determine whether there are significant _______ differences in the population.

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?