Exam 18: Nonparametric Methods

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below. At a significance level of .05, which one of the following statements is correct regarding the following null hypothesis? H₀: D₁ and D₂ are identical probability distributions.

In a manufacturing facility producing fasteners, a foreman suspects that the diameter of the bolts produced by his second-shift workers is greater than the diameter of the bolts produced by his first-shift workers. He takes a sample of five bolts from the first shift and a sample of four bolts from the second shift and measures the diameters in inches. The population of bolt diameter measurements is not normally distributed. Which one of the following nonparametric tests is appropriate for this problem?

The Wilcoxon rank sum test and the Kruskal-Wallis test both require that we take independent random samples.

An international economist believes that there is a significant relationship between the amount of debt and the rate of unemployment. He randomly selected six countries to determine if there is a significant relationship between debt and unemployment rate. In the following table, debt figures for the six countries are given in billions of dollars and the corresponding unemployment rate is given in percentages. He also discovered that both the distribution of debt and the distribution of unemployment rate were highly skewed. Use Spearman's rank correlation and determine if there is a significant correlation between debt and unemployment rate at alpha .05. Show the rank correlation.

Which one of the following nonparametric methods can be used to compare more than two independent populations in a single test?

The EPA has stipulated that the Pollution Standard Index (PSI) for clean air standards is to average no more than 100. A random sample of 9 days for the city of Acme showed PSI readings of 144, 85, 90, 120, 150, 105, 93, 130, and 115. The EPA wants to test to determine if Acme air is dirtier than the stipulated clean air standards. Assume the population of PSI readings is highly nonnormal and state the null hypothesis.

Parametric methods are ________ more powerful than their nonparametric counterparts.

Refer to the MegaStat/Excel output for the Wilcoxon rank sum test given in the table below. At a significance level of .05, which one of the following rejection point conditions is correct regarding the following null hypothesis? H₀: D₁ and D₂ are identical probability distributions.

The Wilcoxon rank sum test requires that two independent samples being compared must have equal sample sizes.

The Spearman's rank correlation test can be used to study the relationship between two ordinal variables.

Five years ago, the average starting salary of a new college graduate with a major in marketing was $34,000. A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 28, 36, 25, 37, 35, 24, 38, 45, 39, 36. The local university wants to determine if the median starting salary for marketing graduates has increased in the last five years. State the alternative hypothesis. Assume that the population of starting salaries in marketing is not normally distributed.

In an effort to improve productivity in its factory, a firm recently instituted a training program for its workers. One of the work crews consisted of 14 workers. Seven workers from this crew were selected at random to attend the training course. All seven workers selected successfully completed the training course. The remaining seven workers served as a control group and did not attend the training course. Three months after the training course, a foreman who did not know which employees attended the training course was asked to rank all 14 employees in terms of their productivity. A rank of 14 indicates the most productive employee in the crew, while a rank of 1 indicates the least productive worker. At α = .05, can it be concluded that training was beneficial in improving productivity?

Which one of the following nonparametric methods requires that we carry out a paired difference experiment?

A readability analysis is conducted to determine how easy four different newspapers are to read for the average citizen. The sample scores are below. Calculate H.

An e-business/e-commerce information technology consulting company wants to compare the effectiveness of three programming languages that its programmers use. Currently each programming language is used by approximately 1/3 of the company's programmers. The director of the programming division randomly selected five programmers from the users of each of the three programming languages and assigned the same simple programming task to each programmer. All three populations have highly skewed distributions with extreme outliers. The rank sum values for each of the programming groups are T₁ = 23, T₂ = 48, and T₃ = 49. At α = .05, does the median time required to program a simple task differ between the three different programming languages?

In a local ice-skating contest, there were two judges and 15 contestants. Each judge was asked to rate each contestant on a 7-point scale. The most successful candidates received a rating value of 7, while the least successful candidates received a rating value of 1. It appears that the bivariate normal probability distribution assumption was severely violated. The City Council wants to know whether the judges have similar opinions in rating ice-skating competitors. At a significance level of .01, the rejection point condition for the hypothesis test is

Which of the following statements about nonparametric methods is correct?

The Kruskal-Wallis H statistic can be approximated by the ________ distribution.

A sign test is a test of hypothesis about the population mean.

An owner of two cats is trying to decide if it is cheaper to order cat food over the Internet or to buy the food locally. Listed below are the prices (in dollars) quoted for two bags of cat food from various manufacturers. Set up the alternative hypothesis for the claim that buying over the Internet (I) is cheaper than buying from the local stores (E).