Answer Happy

Exercise 3 The aim of a study is to investigate whether a new stimulant drug can increase attention and con- centration in subjects suffering of ADHD. A group of researchers conduct an experiment where each participant is given a text to read while music is played into the room. The participant is then given a test afterwards on the contents of the text. The score on the test determines focusing skills and higher score implies better concentration on the reading task. A group of 17 participants were administered the stimulant and tested, and a control group of 21 subjects were not given the drug and tested. The results are as follows: Stimulant drug 57.3 10.8 17 Control 44.5 6.2 21 1. Is there evidence in the data to suggest that the stimulant increases the mean concentration score of more than 10 points? (Take a = 0.01) 2. Construct and interpret a 95% confidence interval for the mean difference in concentration score. 3. The researchers would like to detect an increase of 10 points score with a power of 90% and a significance level of 0.01, knowing from previous studies that the standard deviation of the concentration test score is 12.7. How many subjects do they need to recruit in total? Total: 25 marks] Exercise 4 The average concentration of arsenic pollutants in a river last year has been measured to be of 11.85 parts per billion (pbm). In the current year, a sample of 15 measurements has been collected, giving a an average arsenic concentration of 11.03 pbm, with sample standard deviation 0.89 pbm. 1. Is the average arsenic concentration significantly different from the previous year? Use a signif- icance level of 0.01 and compute the p-value. 2. Compute the 99% confidence interval for the population average arsenic concentration. 3. The U.S. Environmental Protection Agency considers water to be not safe to drink if the average arsenic concentration is greater than 10 pbm. Can the water of the river be considered safe to drink? Use the collected data to answer this question, with a significance level of 0.001 and computing the p-value. [Total: 25 marks]