Answer Happy

10.66 An investigator draws two independent random samples, sample 1 and sample 2, of sizes ni = 170 and n2 = 150 from populations 1 and 2, respectively. These populations are populations of objects of two types, type A and type B. Sample 1 contains 104 objects of type A and sample 2 contains 107 objects of type A. Test the claim that one of the two populations contains a higher proportion of type A objects than the other, and give (a) the test statistic and (b) the P-value of the test. (c) Does the data show definitively which population contains a higher proportion of type A objects? Answer "yes," or "no."

10.56 For the two breeds of hogs in Problem 10.54, test the claim that hogs of breed A tend to show less variability in weight gain than hogs of breed B. Use the F-statistic computed as a fraction with one sample variance in the numerator and the other in the denominator. State the conclusion in words, and state any assumptions required for the validity of the test.

10.60 An elementary school principal wants to compare the learning outcomes of two different methods for teaching first grade children to read. The two methods are phonics and rote. The first graders at the principal's school are randomly assigned to two classes at the beginning of the school year. During that school year, the teacher in one class teaches reading by phonics while the teacher of the other class teaches by the rote method. At the end of the school year the two classes are given a standardized reading test. The scores are presented in Table 12. Does this data give statistically significant evidence that the phonics method tends to produce higher test scores than the rote method? Test at significance level .05, using a one-sided test, and state your conclusion in words. Use the t-test that assumes homoscedasticity. phonics 80 75 68 84 76 76 83 74 76 rote 60 72 81 65 80 63 62 85 70 72 71 77 Table 12: Reading Test Scores

10.62 Referring to Problem 10.60, use a randomization test with 4000 repli- cates to test the claim that the phonics method tends to produce higher scores than the rote method against the null hypothesis prote Mphonics. Give (a) the estimated 1-tailed P-value and (b) the conclu- sion. Before running your program, set the random number seed to 26*y + pos where y is the last digit of the current year and pos is the position in the alphabet of the first letter of your last name.

10.64 A statistics professor teaches two sections of the course Elementary Statistics. One section contains 22 students and meets at 7:45 am and the other contains 19 students and meets at 8:50 am. As an experiment, the teacher allows the 8:50 class to take weekly quizzes in small groups of size 4 or fewer. The other class takes the same quizzes, but is required to complete the quizzes individually. The professor theorizes that group work tends to lead to better learning and will produce better scores on the next hour exam. The professor plans to share his results with his colleagues, some of whom are of the opinion that group work actually leads to less learning. The last hour exam produces the exam scores displayed in Table 13. Group work allowed 74 62 68 59 61 31 42 52 38 44 47 58 49 62 48 58 54 52 3953 41 27 Individual work only 45 52 60 49 32 51 42 37 56 67 41 30 33 41 30 31 45 42 60 Table 13: Group work versus individual (a) Is this a controlled experiment or an observational study? (b) Do these data give statistically significant evidence that group work leads to higher exam scores than individual work does, or does it show the opposite? Answer this question in one or more succinct, statistically literate sentences, basing your answer on an appropriate hypothesis test. (c) Do the data give statistically significant evidence that group work tends to lessen variability in exam scores in a class? Answer this in one or more concise sentences, basing your answer on the classic F-test that uses the test statistic F = si/s. 0