Exam 15: Distribution-Free Procedures

When $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \ldots \ldots \ldots = \mu _ { j }$ is true, and either the number of population or treatment means I = 3 and the sample size $J _ { i } \geq 6$ (i = 1,2,3), or I > 3 and $J _ { i } \geq 5$ (i = 1, ,I), then the Kruskal-Wallis test statistic K has approximately a __________ distribution with __________ degrees of freedom.

Which of the following statements are true?

Suppose that a random sample of size 30 from a normal population is used to test $H_{0}: \mu=50 \text { versus } H_{a}: \mu \neq 50$ The t test at level .10 specifies that $H _ { o }$ should be rejected if the test statistic value t is either $\geq$$\underline{\quad\quad}$ or $\leq$$\underline{\quad\quad}$

For moderate values of the number of blocks J, the Friedman's test statistic $F _ { r }$ has approximately a __________ distribution with __________ degrees of freedom, where I is the number of treatments.

Friedman's test for a randomized block experiment rejects $H _ { 0 } : \alpha _ { 1 } = \alpha _ { 1 } = \ldots \ldots \ldots = \alpha_{j}$ (where $\alpha _ { i }$ is the i th treatment effect) when the computed value of the test statistic $F _ { r }$ is too __________.

In an experiment to compare the bond strength of two different adhesives, each adhesive was used in five bondings of two surfaces, and the force necessary to separate the surfaces was determined for each bonding. For adhesive 1, the resulting values were 240, 297, 256, 310, and 261, whereas the adhesive 2 observations were 224, 190, 174, 258, and 236. Let $\mu _ { i }$ denote the true average bond strength of adhesive type i. Use the Wilcoxon rank-sum test at level .05 to test $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { \pm } : \mu _ { 1 } > \mu _ { 2 } \text {. }$

A random sample of size 15 is drawn from a continuous and symmetric probability distribution with mean $\mu .$ In testing $H _ { o } : \mu = 300 \text { versus } H _ { a } : \mu \neq 300$ using the Wilcoxon signed-rank test with approximate level of significance of .05, the rejection region for the test is

A study reports the accompanying data on lead concentration $( \mu g / L )$ in samples gathered during eight different summer rainfalls: 19.0, 23.4, 32.6, 7.0, 14.2, 13.8, 19.3, and 20.8. Assuming that the lead-content distribution is symmetric, use the Wilcoxon signed-rank interval to obtain a 95% CI for $\mu .$

Suppose $x _ { 1 } = - 8 , x _ { 2 } = 6.5 , x _ { 3 } = 7 , y _ { 1 } = 10 , y _ { 2 } = 6.8 , y _ { 3 } = 8.8 , \text { and } y _ { 4 } = 5.1$ Then, the computed value of the Wilcoxon rank-sum test statistic W is w = __________.

When ranking data in a Wilcoxon signed-rank test, the data value that receives a rank of 1 is the

For any distribution, the asymptotic relative efficiency (ARE) will be at least __________, and for many distributions will be much greater than 1.

The Wilcoxon rank-sum test is applied to three values of x and four values of y. Then, the smallest possible value of the test statistic W is w = __________ and the largest possible value is w = __________.

Which of the following statements are not true?

The Wilcoxon signed-rank interval uses pairwise averages from a single sample, whereas the Wilcoxon rank-sum interval uses pairwise differences from __________ samples.

Because the t and F procedures are based on a particular parametric family of distributions (normal), they are not __________ procedures.

Two independent random samples of sizes 5 and 7 are selected from two continuous distributions with means $\mu _ { 1 } - \mu _ { 2 } ,$ and that the two distributions have the same shape and spread. In testing $H _ { o } : \mu _ { 1 } - \mu _ { 2 } = 0 \text { versus } H _ { \pm } : \mu _ { 1 } - \mu _ { 2 } \neq 0$ using the Wilcoxon rank-sum test with approximate significance level of .05, the rejection region for the test is

Which of the following statements are not true?

A random sample of 15 automobile mechanics certified to work on a certain type of car was selected, and the time (in minutes) necessary for each one to diagnose a particular problem was determined, resulting in the following data: 32.6 32.1 17.6 28.7 29.1 27.4 37.0 32.8 33.9 55.2 14.5 25.2 10.8 26.9 32.2 Use the Wilcoxon test at significance level .10 to decide whether the data suggests that "true" average diagnostic time is less than 32 minutes.

The accompanying data resulted from an experiment to compare the effects of vitamin C in orange juice and in synthetic ascorbic acid on the length of odontoblasts in guinea pigs over a 6-week period. Use the Wilcoxon rank-sum test at level .01 to decide whether true length differs for the two types of vitamin C intake. Compute also an approximate P-value. Orange juice 8.5 9.7 9.9 10.0 10.3 14.8 15.5 16.4 17.9 21.8 Ascorbic acid 4.5 5.5 6.1 6.7 7.3 7.6 10.4 11.5 11.6 11.8

Which of the following statements are not true?