Exam 19: Nonparametric Statistics

The population Spearman correlation coefficient is labeled ____________________ and the sample statistic used to estimate its value is labeled ____________________.

In a Wilcoxon rank sum test,the two sample sizes are 4 and 6,and the value of the Wilcoxon test statistic is T = 20.If the test is a two-tail and the level of significance is $\alpha$ = 0.05,then:

When n > 30,r_s has an approximate normal distribution with mean ____________________.

The Wilcoxon signed rank sum test incorporates not only the sign of each difference,but the ____________________ of the difference as well.

A one-sample t-test is the parametric counterpart of the Kruskal-Wallis test.

One of the required conditions of the sign test is that the number of nonzero differences n must be greater than or equal to 30.

Frozen TV Dinner The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market.He decides to perform an experiment to help make a decision.Each dinner is sampled by ten people who then rate the product on a 7-point scale,where 1 = poor,and 7 = excellent.The results are shown below. Tasts Ratings Respondent Dinner 1 Dinner 2 Dinner 3 Dinner 4 1 6 6 4 5 2 5 5 2 4 3 7 7 3 4 4 6 6 5 4 5 7 6 4 3 6 7 5 3 5 7 6 4 3 4 8 5 6 4 6 9 4 4 3 5 10 7 5 6 4 -{Frozen TV Dinner Narrative} Can the general manager infer at the 5% significance level that there are differences in the taste ratings of the four dinners?

Airlines Ranking Ten business people who fly frequently from Las Vegas to Miami were asked to rank four airlines in terms of the quality of service.The people assigned scores using a 5-point Likert scale where: 1 = bad,2 = poor,3 = average,4 = good,and 5 = excellent.The results are shown below: Airline Person A B C D 1 1 3 5 2 2 5 4 2 1 3 2 5 3 2 4 4 2 4 1 5 3 3 1 5 6 4 4 5 3 7 3 4 1 4 8 2 5 2 1 9 5 3 4 2 10 5 5 4 3 -{Airlines Ranking Narrative} Can we conclude at the 5% significance level that there are differences in service quality among the four airlines?

Keyboard Speed Ten administration assistants were selected at random from a large university.The keyboard speed (number of words per minute)was recorded for each secretary on two different brands of computer keyboards.Assume that the typing speeds are not normally distributed.The following results were obtained. Computar Kayboard Sacretary Brand A Brand B Barry 72 74 Betty 80 86 Caral 68 72 Cliff 74 70 Ellen 86 85 Fred 75 73 Gwen 78 72 Harry 69 65 Ingrid 76 79 Jerome 65 64 -{Keyboard Speed Narrative} Perform the sign test to determine if these data provide enough evidence at the 5% significance level to infer that the brands differ with respect to keyboard speed.

The population Spearman correlation coefficient is labeled $\rho$ _s,and the sample statistic used to estimate its value is labeled r_s.

The test statistic F_r for the Friedman test has what distribution?

Which of the following will never be a required condition of a nonparametric test?

Consider the following data set: 14,14,15,16,18,19,19,20,21,22,23,25,25,25,25,and 28.The rank assigned to the four observations of value 25 is:

The data for analysis by a Friedman test are either ordinal or interval,but they do not have a(n)____________________ distribution.

Suppose using Kruskal-Wallis test,there are five samples,and the value of the test statistic is calculated as H = 12.32.Then the most accurate statement that can be made about the p-value of the test is that it is greater than 0.025 but smaller than 0.05

To determine if a relationship exists between two variables,the hypotheses to be tested are H₀: r_s = 0 vs.H₁: r_s $\neq$ 0.

Some statistical software perform the Mann-Whitney test.However,this test and the sign test are equivalent tests.

Advertisement In a Kruskal-Wallis test to determine whether differences exist among three different advertisements,the following statistics were obtained: T₁ = 884,n₁ = 20,T₂ = 756,n₂ = 28,T₃ = 1061,n₃ = 25. -{Advertisement Narrative} What is the most accurate statement that can be made about the p-value of this test?

An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows. Contestant Years af Education Winnings 1 11 750 2 15 400 3 12 600 4 16 350 5 11 100 6 16 300 7 13 650 8 14 400 Can she conclude at the 5% significance level that the more educated the contestant,the less the money he or she wins in TV game shows? (The condition of normality is not met by these variables. )

Each year the human resources department in a large corporation assesses the performance of all of its employees.Each employee is rated for various aspects of his or her job on a 7-point scale where 1 = very unsatisfactory and 7 = satisfactory.The CEO of the company believes that the assessment scores this year are lower than last year's.To examine the validity of this belief she draws a random sample of six employees' scores from last year and another six employees' scores this year.Do the data listed below allow the CEO to conclude at the 5% significance level that her belief is correct? Employess Ratingr Feores This Year Last Year 5 5 6 5 4 3 5 3 5 4 4 3