5. An experiment compared the ability of three groups of subjects to remember briefly-presented chess positions. The data are shown below. (One-Way Anova) Non-players Beginners Tournament players 22. 132.5 40.1 a. Using the Tukey HSD procedure, determine which groups are 223 37.1 45.6 significantly different from each other at the .05 level. 26.2 51.2 b. Now compare each pair of groups using t-tests. Make sure to 29.6 40.5 56.4 control for the familywise error rate (at 0.05) by using the Bonferroni 31.7 45.5 58.1 correction. Specify the alpha level you used. 33. 51.3 71.1 38.9 52.6 749 39 7 55.7 75.9 43.2 155.9 80.3 43.2 157.7 8523 6. In a study of the cognitive capacities of nonhuman primates, 19 monkeys of the same age were randomly divided into two groups of 10 and 9. The groups were trained using two different teaching methods to recollect an acoustic stimulus. The monkeys' scores on a subsequent test is given below. Method 1: 167, 149, 137, 178, 179, 155, 164, 104, 151, 150 Method 2: 98, 127, 140, 103, 116, 105, 100, 95, 131. Analyze the data to test if one method works better than the other. What assumptions do you need to make in your analysis? How can you argue for these assumptions? 7. Two types of smudge pots were tested for use to protect orchards from frost. A grapefruit grower wants to compare them in terms of how long they burn before dying out. Two samples of burning times for 10 smudge pots each are recorded below. It is desired to test whether or not there is a difference between mean burning times for the two types of smudge pot. The burning times (in minutes) were: Type 1: 612 583 629 595 653 596 624 564 576 593 Type 2: 592 607 696 686 680 669 697 729 694 662 (i) Assume that the data behave as if they were two independent random samples from two different normal populations with the same variance. State the appropriate null and alternative hypothesis, and test the null hypothesis at alpha=0.05. What is the resulting P-value? (Hint:: The first sample has mean 602.50 and sample standard deviation 26.99. The second sample has mean 671.20 and sample standard deviation 42.06. ) (ii)What test statistic did you use? What is its distribution under the null hypothesis? (iii)Find a 95% confidence interval for the difference in mean burning time between the two types of pot. 8. You are working on a magic pill that you think might totally eliminate pain when given to patients who are experiencing severe pain In your work, you have discovered three ingredients that might be effective if each is