Exam 20: Nonparametric Tests

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.Since the number of heads and tails are larger than 10,the test statistic R can be assumed to follow a normal distribution.The value of the test statistic is _____.

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 seven packages shipped. Using the critical value approach and α = 0.10,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 critical 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 critical 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. The estimate of the population proportion of plus signs 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. For the Wilcoxon signed-rank test for the matched-pairs sample,the competing hypotheses are ________________________.

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. To determine whether the median return of growth funds is larger than the median return of value funds,the competing hypotheses are ___________.

A trading magazine wants to determine the number of hours stockbrokers work each week.In particular,the trading magazine wants to determine if the median number of hours 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 T = T⁺ = 153.At the 1% significance level,the critical value is _____.

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

The nonparametric test to determine if a sequence is random 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. Assuming has the standard normal distribution,the value of the test statistic for the sign test is __________.

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. The p-value for the test 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.At the 10% significance level,the critical value is _____.

The Kruskal-Wallis test is a nonparametric alternative to the _________ test that can be used when the assumptions of normality and/or equal population variances cannot be validated.

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 r_s = 0.47. 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?

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.To determine if the SHY is not a market-neutral position,the competing hypothesis are __________.

A trading magazine wants to determine the number of hours stockbrokers 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 T = T⁺ = 153.Inasmuch as the sample size is more than 10,T can be assumed normally distributed with mean and standard deviation ___________,respectively.

If we wish to compare central tendency from nonnormal population,then the Wilcoxon signed-rank test serves as the nonparametric counterpart to the __________ test.

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. At the 5% significance level,the critical value is ______.

Nonparametric tests do not require a level of measurement as strong as it is necessary for parametric tests.