an environmental company is studying water samples from 80 lakes for pollution. five of the lakes have high levels of dioxin. if six lakes are randomly selected, how many ways could one pollujted lake and five non-polluted lakes be chosen

A consumer agency wants to determine which of two laundry detergents, A or B, cleans clothes better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be 1.5. Assuming there is no difference in the two detergents, 200 simulated differences in sample mean ratings are displayed in the dotplot.   Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other? Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that A is more effective…

600 students at Drew High School were surveyed. 269 of them were males. 455 of the students' wear jewelry, and 300 of the students that wear jewelry are females.

You are interested in testing if there is a difference in weight-loss between 3 popular diet types; low calorie, low fat and low carb. Participants are randomly assigned one of the three groups or a control group. The control group will be told that are participating in a weight-loss study, but will not be following any particular diet. This is to study the placebo effect, weight-loss from just participating in the study. At the start of the study, each participant's weight is recorded in pounds. After 8 weeks they are weighed again, and the weight difference is recorded. A positive value represents a weight loss while a negative value represents a weight gain. Test at 5% significance. Round answers to 3 decimal places. Diet Type Low Calorie Low Calorie Low Calorie Low Calorie Low Calorie Low Fat Low Fat Low Fat Low Fat Low Fat Low Carb Low Carb Low Carb Low Carb Low Carb Control Control Control Control Control Pounds Lost 6.9 4.7 3.5 7.7 5.9 3.8 1.4 3.8 5.2 2 4.9 2.6 2.7 5.6 3.4 1.3…