Exam 20: Nonparametric Tests

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 ________.

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 the sampling distribution of can be approximated by the standard normal distribution, the value of the test statistic 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 value of the test statistic W 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 are 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. For the Wilcoxon signed-rank test for the matched-pairs, 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. To test the random-walk hypothesis about oil production, the competing hypothesis are ________.

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. The value of the test statistic is ________.

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

In the Wald-Wolfowitz test a ________ is an uninterrupted sequence of one letter, symbol, or attribute.

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds are 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. Assuming that the sampling distribution of T can be approximated by the normal distribution, the value of the z test statistic is ________.

An airline claims that the median price of a round-trip ticket is less than $503. For a random sample of 400 tickets, the value of the Wilcoxon sign-ranks test is T = T⁺ = 37,230. A) Specify the competing hypothesis to determine whether the median ticket price is less than $503. B) Assume the normal approximation for the distribution of T, and calculate the value of the corresponding test statistic. C) At the 10% significance level, what is the decision and conclusion?

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. To determine if the weights and costs are significantly correlated, the competing hypothesis is ________.

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. If the sampling distribution of T can be approximated by the normal distribution, the value of the z test statistic is ________.

Nonparametric tests do not require data of interval or ratio scale.

Nonparametric tests use fewer and weaker ________ than those associated with parametric tests.

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?

Parametric tests are distribution-free tests.

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. Given the sample size, the sampling distribution of r_s can be approximated by the normal distribution with standard deviation ________.

If we have a matched-pairs sample of ordinal data, we can use the sign test to determine whether there are significant differences between the ________.

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. Using the critical value approach and α = 0.01, the appropriate conclusion 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. The p-value for the test is ________.