Exam 18: Nonparametric Methods

Wax-com Electronics Inc. claims that a certain circuit board has a median operating life of less than 20,000 hours. A random sample of 25 such circuit boards showed 8 circuit boards failing before 20,000 hours and 17 circuit boards failing after 20,000 hours. Assume the useful life of the circuit board is not normally distributed. At α = .05, can it be concluded that the sample contradicts the company's claim? Assume the useful life of the circuit board is not normally distributed.

The ________ detects whether the probability distribution of one population is shifted to the right or to the left of the probability distribution of another population.

Parametric tests, such as F and t tests, are more powerful than their nonparametric counterparts if the assumptions needed to perform the parametric test are not violated.

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. Assume the population of PSI readings is highly nonnormal. Is there significant evidence to conclude that Acme air is dirtier than the stipulated clean air standards? Test at α = .05.

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. State the null hypothesis for this problem.

The sign test is a nonparametric test for a population mean that is valid for any sample size and population shape.

A local real estate agent claims that the median selling price of homes in a major midwestern city is more than $200,000. Suppose a random sample of 100 homes sold in the last six months is taken and 53 sold for over $200,000. State the null hypothesis to test the claim. Assume that the population of selling prices is not normally distributed.

The sign test is a test about a population median that is valid for any sample size and population shape.

A parametric test is always more powerful than its nonparametric counterpart.

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. Assume that the population of starting salaries in marketing is not normally distributed. Using α = .05, can we conclude that the starting salaries increased in the last five years?

Assume that the following data set is not normally distributed. (21, 18, 4, 9, 14, 16, 17, 12, 15, 8, 7, 5) If H_a: M_d > 6, then the p value is

A professional organization is attempting to determine whether salaries of hospital CFOs differ by geographical region. Five hospital CFOs were randomly selected from each of the following four regions of the United States: East, Midwest, South, and West. Each CFO was then asked his or her annual salary. The salary distributions were highly skewed. The table below summarizes the results of the Kruskal-Wallis test obtained from MegaStat/Excel. Kruskal-Wallis Test At a significance level of .05, the rejection point condition for the hypothesis test is

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: 38, 36, 25, 37, 35, 24, 38, 45, 39, 36. The local university wants to determine if the starting salaries have increased in the last five years. Assume that the population of starting salaries in marketing is not normally distributed. Which one of the following tests is appropriate for this problem?

A copy machine service company provides maintenance and repair service for different types and brands of copiers. The manager of the repair department wants to know if the repair time for brand A is higher than the repair time for brand B. The manager randomly selected eight repair records associated with brand A and eight repair records associated with brand B. The repair times (in minutes) for both samples are given below. The distribution of repair times for both brand A and brand B is highly skewed. On average, can it be concluded that the repair time for brand A is significantly higher than the repair time for brand B? Test at α = .05.

Two coffee-vending machines are studied to determine whether they distribute the same amounts. Samples are taken and the number of ounces is recorded for each machine. What is the appropriate null hypothesis for the claim that they distribute the same amount of coffee?

A copy machine service company provides maintenance and repair service for different types and brands of copiers. The manager of the repair department wants to know if the repair time for brand A is higher than the repair time for brand B. The manager randomly selected eight repair records associated with brand A and eight repair records associated with brand B. The repair times (in minutes) for both samples are given below. The distribution of repair times for both brand A and brand B is highly skewed. What is the appropriate alternative hypothesis for this problem?

The Wilcoxon signed ranks test is also called the Mann-Whitney test.

A cholesterol test was given to 10 heart patients with high cholesterol levels. The same 10 heart patients are then given a new cholesterol-reducing drug for six months. Before the patients begin taking the drug, they are told to maintain their current diets and eating habits so that the effect of the drug can be more effectively determined. After taking the drug for six months, the same patients are given a cholesterol test again. The pharmaceutical company manufacturing the medicine wants to know if the drug is effective in reducing the cholesterol levels of the patients. The cholesterol levels before and after taking the drug are recorded for each patient. The population of cholesterol levels is not normally distributed. Which one of the following nonparametric tests is appropriate for this problem?

Which one of the following nonparametric methods can be considered as an extension of the Wilcoxon rank sum test?

A random sample of 11 third-year medical school students took a comprehensive written exam as well as a comprehensive oral exam. The scores on both exams are given below. It is established that both test scores have highly nonnormal distributions. The medical examination board wants to know if the oral exam scores are higher than the written exam scores. State the appropriate null hypothesis for this problem.