AP Statistics Ch. 12 Graded Worksheet Name:____________________________ 1. In baseball, hits can be one of four types: singles, doubles, triples, or home runs. In the last baseball season, 64% of the hits were singles, 20% were doubles, 2% were triples, and 14% were home runs. Spring training games are played in March before the regular season to help the players get in shape. A sports writer thinks that perhaps the distribution of types of hits is different in these games. The sportswriter gathers a random sample of 251 hits from spring training games. Here is the distribution of types of hits for these games: Singles Doubles Triples Home Runs 153 59 5 34 At the .05 level of significance, test the hypothesis that the proportions of the different types of hits in the spring is the same as for last year's season. (Full phantom!) 2. As every airline passenger knows, there are never enough armrests! Over the course of 20 flights occurring over a variety of weekdays, nights, and weekends, researchers selected a random sample of passengers that had been seated next to individuals of opposite gender. The passengers were surveyed as they left the boarding area. The researchers were interested in the level of agitation felt when their "seat‐mate" used the common armrest. Only one person was randomly selected to be interviewed from a seat‐mate pair, and couples were excluded from the survey. The question of interest was whether males and females are equally bothered by their opposite gender's use of the common armrest. The table below summarizes data gathered from interviewing the passengers. State of Bother vs. Gender Bothered Not bothered Females 19 26 Males 38 18 a) What is the appropriate null hypothesis for this investigation? (You may state this hypothesis in ordinary English if you wish.) b) Using the hypothesis from part (a), test the null hypothesis using the appropriate chi‐square procedure. (Full phantom!) 3. The authorship of ancient writings is frequently in dispute. One method for judging authorship of writings from the Classical Greek period is to analyze the proportion of sentences containing the word,   . (   is an article, something like "a," "an," and "the" in English.) If a particular collection of works has markedly different frequencies of use of   , this would be considered evidence against the same author having written all the works. In the table below, data from random samples of 200 sentences each from 4 works are presented. The alleged author is one Philo Judaeus (c. 30 BCE – CE 45), a philosopher writing in ancient Alexandria, Egypt. Gar sentences Number of Number of Number of Sample sentences sentences sentences with   without   in sample On the Cherubim 37 163 200 Sacrifices of Abel and Cain 43 157 200 Worse Attacks the Better 50 150 200 The Posterity of Cain 46 154 200 At the .05 level of significance, test the hypothesis that the frequencies of the use of   is the same for these 4 works. Do not do full phantom!!!! Write Ho/Ha, find Chi‐squared, find p, and make conclusion.