Exam 18: Nonparametric Tests

An advantage of nonparametric tests is that they require less stringent assumptions than parametric tests.

When evaluating differences among more than two populations, the appropriate nonparametric test is the Kruskal-Wallis test.

If the $U$ test is applied in a test whose alternative hypothesis is $\mu_{1} \neq \mu_{2}$ with $n_{1}=7, n_{2}=7, \alpha=0.05$ , the null hypothesis can be rejected if

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 large 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 $\mathrm{H}$ test is another name for the __________ test.

A company that makes foot-long hot dogs requires that the median lengths of its hot dogs be 12 inches. A sample of 18 hot dogs produced by this company in order actually have lengths in inches: 10,11,13,13, 14, 12, $11,9,13,12,14,13,11,13,14,10,14,15$ . Does this data provide sufficient evidence to indicate a lack of randomness in the pattern of too short and too long hot dogs? Use $\alpha=0.05$ .

The sign test is used with $n=9$ to test the null hypothesis that the new method and the old method produce equally high scores against the alternative hypothesis that the new method produces higher scores than the old. If we obtain eight plus signs in subtracting (new score - old score), then with $\alpha=0.05$ , the null hypothesis should

Students were observed as they arrived at a college dance. The following is the order in which men and women arrived at the dance: $M M M M M W M M W W$ $M M M W M W W M M M$ Test the sequence for randomness at the 0.05 level of significance.

In the $U$ test, $U_{1}$ and $U_{2}$ take on values between __________ and __________, and their sum always equals __________.

Table 18.2 -Table 18.2 shows the scores made on the verbal and mathematical components of an S.A.T. by 15 high -school seniors who plan to go to a certain college. Use the table to calculate the Spearman Rank-Correlation Coefficient for the test scores.

Suppose we want to test whether or not two samples come from the same population. If the assumptions of the standard test for the difference between two large sample means (given in Chapter 11) are satisfied, and we are to choose either that test or the U test, which one should we choose? Why?

Which of the following tests must be two-tailed?

In the $U$ test, the statistic $U$ is always the larger of $U_{1}$ and $U_{2}$ .

If there were an extremely large or small number of runs in the data, then we would be more likely to believe that the data is random.

The Kruskal-Wallis test involves an application of the

For a ranked sample of size $n$ , the sum of the ranks is __________.

Independent random samples of eight males and seven female students at a college showed the following weekly food expenses in dollars. Men: $20,21,25,28,30,28,24,26$ Female: $25,18,17,23,20,24,22$ Test the null hypothesis that the men and women have the same average food expenses against the alternative hypothesis that they do not have the same average food expenses. Use $\alpha=0.05$ .

The Mann-Whitney test is the same as the

The runs test is a test for __________.

Nonparametric methods are usually less efficient than parametric methods.