Exam 18: Nonparametric Methods

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 non-normal 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.

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

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

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 test statistic T?

When a large sample is taken,_______________ approximation to the binomial distribution can be used to implement the sign test.

The __________________ test is a nonparametric counterpart of a small sample t test for comparing two independent population locations.

A student is trying to decide if it is cheaper to order blank CDs over the internet or to buy them at local electronic stores.Listed below are the prices (in dollars)quoted for boxes of 200 blank CDs from various manufacturers. What is the test statistic T?

Which of the following statements about nonparametric methods is correct?

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 value of S is:

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?

The EPA has stipulated that the PSI,"Pollution Standard Index" for clean air standards is to be no more than 100 on the average.A random sample of 9 days for the city of Acorn showed PSI readings of 144,85,90,120,150,105,93,130 and 115.Assume the population of PSI readings is highly non-normal.EPA wants to determine if there is significant evidence to conclude that Acorn's air is dirtier than the stipulated clean air standards.Which one of the following tests is appropriate for this problem?

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 cholesterol levels before and after taking the drug is given below.Distribution of cholesterol level is not normally distributed.At $\alpha$ = .05,test to determine if the drug is helpful in reducing cholesterol levels.

Nonparametric tests can be more powerful than the corresponding t or F tests if the population distribution is highly skewed or nonnormal.

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 than asked his or her annual salary.The distributions of salaries were highly skewed.The table below summarizes the results of the Kruskal-Wallis test obtained from Mega-Stat/Excel. At a significance level of .05,the rejection point condition for the hypothesis test is:

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 programmers employed by the company.The director of programming division randomly selected 5 programmers from the users of each of the three programming languages and assigned the same simple programming task to each programmer.It is known that 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 $\alpha$ = .05,does the median time required to program a simple task differ between the three different programming languages?

Refer to the Mega-Stat/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 is shifted to the left of D₂

The Wilcoxon rank sum test is the nonparametric counterpart of the:

In order to perform the ________________ test,all of the observations in two samples are combined into a single set and all of the values in the single set are ranked from smallest to largest.

A ______ test is a statistical test that can be used without assuming that the sampled population(s)have a particular type of probability distribution.

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 $\alpha$ = .05,can it be concluded that the sample contradicts the claim of the company?