Exam 15: Distribution-Free Procedures

A 95% distribution-free confidence interval for a parameter $\theta$ can be obtained from a level __________ test for $H _ { 0 } : \theta = \theta _ { 0 } \text { versus } H _ {a } : \theta \neq \theta _ { 0 }$

A Study of Wood reports the following data on burn time (hours) for samples of oak and pine. Test at level .05 to see whether there is any difference in true average burn time for the two types of wood. Oak 1.80 .75 1.63 1.64 4.50 1.31 1.85 .56 Pine 1.06 1.48 1.41 1.60 .81 1.28

When $H _ { 0 } : \alpha _ { 1 } = \alpha _ { 1 } = \ldots \ldots \ldots = \alpha _ { 10 }$ is tested using the Friedman's test statistic $F _ { r }$ with significance level .025 (where $\alpha _ { i }$ is the i th treatment effect), then $H _ { 0 }$ is rejected if $F _ { r }$ is greater than or equal to __________.

The accompanying data refers to concentration of the radioactive isotope strontium-90 in milk samples obtained from five randomly selected dairies in each of four different regions. 7.0 6.4 7.1 8.3 6.7 Region 7.7 10.5 11.8 11.1 9.4 6.3 6.5 8.8 7.2 5.7 10.1 12.7 10.9 13.0 12.3 Test at level .10 to see whether true average strontium-90 concentration differs for at least two of the regions.

Let $x _ { 1 } , x _ { 2 } , \ldots , x _ { 10 }$ be a random sample from a continuous and symmetric probability distribution with mean (and median) $\mu .$ In testing $H _ { o } : \mu = 100 \text { versus } H _ { a } : \mu > 100$ using the Wilcoxon signed-rank test, the rejection region for level .01 test is $s _ { + } \geq$$\underline{\quad\quad}$

Compute the 90% rank-sum CI for $\mu _ { 1 } - \mu _ { 2 }$ using the following data: Sample A: 229 286 245 299 250 Sample B: 213 179 163 247 225