Exam 14: Nonparametric Statistics Available Online

A government agency claims that the median hourly wages for workers at fast food restaurants in the western U.S. is $8.20. In a random sample of 100 workers, 68 were paid less than $8.20, 10 were paid $8.20, and the rest more than $8.20. Test the governmentʹs claim. $\text { Use } \alpha = .05 \text {. }$

Do popular diets really help customers in the long-run? Many diets help customers lose weight initially only to have the customer add the weight back on after the first few months on the diet. A Commercially successful diet company conducted a study of twelve randomly selected customers And measured their weight after before starting the diet and then again after staying with the diet For a year. The company hoped that the initial weight loss would be sustained after the first year on The diet. The data is shown below: Customer Initial One Year 1 185 175 2 192 193 3 125 115 4 148 146 5 165 170 6 220 175 7 265 170 8 177 174 9 302 266 10 112 116 11 154 148 12 230 256 What alternative hypothesis should be tested in order to determine if the diet is successful at helping customers lose and keep weight off after one year?

Specify the rejection region for the Wilcoxon rank sum test in the following situation. $n 1 = 7 , n _ { 2 } = 5 , \alpha = .05$ $H _ { 0 }$ : Two probability distributions, 1 and 2 , are identical $H _ { \mathrm { a } }$ : Probability distribution of population 1 is shifted to the right of the probability distribution for population 2

The results of independent random samples from two populations are shown below. Sample A: 11, 15, 18, 21 Sample B: 9, 12, 15, 17, 20, 23 Calculate the rank sum for each sample. Which would be used as the test statistic in a Wilcoxon rank sum test?

A scientist is hoping to compare the levels of DDT toxin found in three species of fish in a local river. He randomly samples 50 of each species to use in the analysis. For each fish, he measures the Amount of DDT toxin present. Ideally he will be able to determine if a difference exists in the Population of DDT toxins found in the three fish species. What type of nonparametric analysis Should be used?

The time (in minutes)it takes to assemble a computer component for three different machines is listed below. Workers are randomly selected. Use the Kruskal-Wallis test to test the claim that there is no difference in the distribution of the populations. $\text { Use } \alpha = .05 \text {. }$ Machine 1 Machine 2 Machine 3 26 34 22 25 23 19 26 32 23 24 27 25 27 29 24 25 26 21 26 30 31

Which of the following is unknown, in general?