Exam 18: Nonparametric Tests

A test was conducted to compare the miles per gallon obtained by three sub-compact automobiles. The following data (in miles per gallon) were obtained from 6 full tanks of the same gasoline. I. $24,22,23,25,22,21$ II. $23,22,26,24,27,25$ III. $30,28,26,27,26,24$ Use a nonparametric test to evaluate whether or not there are significant differences in gasoline economy among the automobiles. Use $\alpha=0.05$ .

The nonparametric alternative to the one-way analysis of variance is the

An aptitude test is given to trainees on a high-tech form. Here are the grades on the test in the order that the trainees completed the test: $98,92,95,85,80,78,75,83,82,95,92,87,80,65,92,93,82,98,93,72,70$ . Test whether the trainees finished the test in random order with regard to grades. Use $\alpha=0.01$ .

The nonparametric alternative to the two-sample $t$ test for the difference between two independent means is the

In the Kruskal-Wallis test, all terms involving ties are eliminated from consideration.

The following are monthly sales (in thousands of dollars) of two department stores, A and B, for the months January through December 1979: 10 and 9,7 and 4,8 and 5, 7 and 6,11 and 10,15 and 16, 15 and 13,12 and 13,9 and 8,18 and 17,19 and 13,21 and 20. -For the situation above, use the small sample sign test with $\alpha=0.05$ to test the null hypothesis that on the average the two department stores have equal sales against the alternative that on the average a. department store $\mathrm{A}$ has more sales. b. there is a difference in sales between the two stores.

The $\mathrm{X}^{2}$ approximation should only be used in the $\mathrm{H}$ test if each sample has more than five items.

Two examples of rank sum tests are __________ and __________.

Random samples of 15 Model I cars and 13 Model II cars were obtained and the number of miles (in thousands) that each lasted from new until the car was "junked" was recorded. Model I: $\quad 70,60,80,75,81,73,80,90,82,93,89,95,91,88,90$ Model II: $\quad 88,80,95,105,90,99,93,88,95,102,98,95,91$ Test the null hypothesis that the two models have the same average life expectancy against the alternative hypothesis that they do not have the same average life expectancy. Use $\alpha=0.01$ .

A nonparametric measure of the association between two variables is called the __________.

The null hypothesis in the runs test is that the sequence of observations is __________.

Suppose that the $U$ test is to be applied to the following sequence. The correct rankings in order are

In a U test, the large sample statistic can be applied if $n_{1}$ __________ and $n_{2}$ __________.

Table 18.1 -The mathematics S.A.T. scores and college grade point averages of eight students are given in table 18.1. a. Calculate the rank-correlation coefficient $r_{S}$ . b. Test the null hypothesis of no correlation using $r_{\mathrm{S}}$ . Let $\alpha=0.05$ .

The application of the $U$ test requires that the two independent samples have the same sample size.

Table 18.3 A consumer advocate is interested in testing whether the number of french fries in a portion in a particular cafeteria is different from that of a particular restaurant. The table below shows the results when random samples of 10 portions of french fries are selected and fries counted. -Use Table 18.3 to conduct the test using $\alpha=0.01$ .

The use of $H$ test requires the assumption that the independent random samples come from identical populations.

In a one-sample sign test, the null hypothesis can be written as __________ or __________.

When we are comparing two populations and our two samples are such that each element of one sample relates to a particular element of the other sample, an appropriate nonparametric test would be the

In applying the number of runs test to the sequence $15,10,13,20,28,30,11,17,9$ , the value of $u$ is __________.