A robbery has been committed and McGuff, the crime-fighting dog, has been called in to investigate. He discovers that Sally Coldhands was seen wearing gloves in the neighborhood shortly after the crime, and, thus, he concludes that she should be arrested. From past experience you know that 50% of the peo- ple that McGuff says should be arrested for robbery are actually guilty. Before making the arrest, you order some additional investigation. From a large population of convicted robbers, you find that 60% wore gloves at the time of the crime and continued to wear them for an interval after the crime. Fur- ther investigation reveals that 80% of the people in the neighborhood of the crime were wearing gloves around the time of the crime. a. Based on the fact that Sally was wearing gloves, what is the probability that Sally actually commit- ted the crime? b. If you charged her with the crime, do you think a jury would convict her based on the glove evi- dence? Explain why or why not.

The director of library services at a college did a survey of types of books (by subject) in the circulation library. Then she used library records to take a random sample of 888 books checked out last term and classified the books in the sample by subject. The results are shown below. Subject Area Percent of Books on Subject in CirculationLibrary on This Subject Number of Books inSample on This Subject Business 32% 247 Humanities 25% 209 Natural Science 20% 222 Social Science 15% 127 All other subjects 8% 83 Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the distribution of books checked out by students. (a) What is the level of significance?State the null and alternate hypotheses. H0: The distributions are the same.H1: The distributions are different.H0: The distributions are different.H1: The distributions are different.    H0: The distributions are the same.H1: The distributions are the same.H0: The…

An anger-management course claims that, after completing its seminar, participants will lose their tempers less often. Always a skeptic, you decide to test this claim. A random sample of 12 seminar participants is chosen, and these participants are asked to record the number of times that they lost their tempers in the two weeks prior to the course. After the course is over, the same participants are asked to record the number of times that they lost their tempers in the next two weeks. The following table lists the results of the survey. Using these data, test the claim at the 0.01 level of significance assuming that the population distribution of the paired differences is approximately normal. Let participants before completing the anger-management course be Population 1 and let participants after completing the anger-management course be Population 2. Number of Times Temper Was Lost during a Two-Week Period Before 10 6 8 10 6 3 10 3 8 After 6 7 4 4 8 6 4 9 3 7 Copy Data Step 2 of 3:…

An anger-management course claims that, after completing its seminar, participants will lose their tempers less often. Always a skeptic, you decide to test this claim. A random sample of 12 seminar participants is chosen, and these participants are asked to record the number of times that they lost their tempers in the two weeks prior to the course. After the course is over, the same participants are asked to record the number of times that they lost their tempers in the next two weeks. The following table lists the results of the survey. Using these data, test the claim at the 0.01 level of significance assuming that the population distribution of the paired differences is approximately normal. Let participants before completing the anger-management course be Population 1 and let participants after completing the anger-management course be Population 2.  Number of Times Temper Was Lost during a Two-Week Period Before 6 7 10 11 8 12 9 8 3 7 11 12 After 5 5 11 8 8 8 6 9 4 6 9 12…

A local health department believes that a store is merchandising its cereal aisle in a way that puts sugary cereal brands at eye level for children. The store claims that it is not considering sugar content and is stocking the shelves based on other factors. An inspector visited the store and recorded the sugar content per serving listed on the boxes (sugar content for each box is listed under the shelf where that box of cereal is located). Shelf 1 Shelf 2 Shelf 3 Shelf 4 7 13 6 10 8. 5 14 7 8 11 11 10 11 3 a) What are the treatment groups, and how many experimental units are there per treatment? b) If instead of using the content listed on the box, the inspector sampled from multiple boxes of each brand of cereal and tested them for sugar content. How many experimental units were there be if there were 10 boxes per brand on the shelf? Explain your answer. [hint: all the boxes for each brand will be in one place] c) State the null hypothesis and create an ANOVA table based on sugar…

The director of library services at a college did a survey of types of books (by subject) in the circulation library. Then she used library records to take a random sample of 888 books checked out last term and classified the books in the sample by subject. The results are shown below. Subject Area Percent of Books on Subject in CirculationLibrary on This Subject Number of Books inSample on This Subject Business 32% 237 Humanities 25% 220 Natural Science 20% 223 Social Science 15% 128 All other subjects 8% 80 Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the distribution of books checked out by students. (a) What is the level of significance?State the null and alternate hypotheses. H0: The distributions are the same.H1: The distributions are different.H0: The distributions are the same.H1: The distributions are the same.    H0: The distributions are different.H1: The distributions are different.H0: The…

In a US presidential election, the incumbent president wins with 51.5% of the vote to 48.2% for the primary challenger (and .3% to others). In a nationwide telephone poll of 1000 people conducted exactly one week before the election by a university polling group, 49% of people polled supported the incumbent president, 50% supported the challenger, and 1% supported other candidates. a. For the polling study, what was the population of interest? b. What was the sample? c. Why did the sample results differ from the population? d. What are two constants that might have limited the generalizability of the polling results?

You may need to use the appropriate technology to answer this question. During the first 13 weeks of the television season, the Saturday evening 8:00 p.m. to 9:00 p.m. audience proportions were recorded as ABC 31%, CBS 26%, NBC 27%, and independents 16%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 97 homes, CBS 68 homes, NBC 91 homes, and independents 44 homes. Test with a = 0.05 to determine whether the viewing audience proportions changed. State the null and alternative hypotheses. 0.31, PCBS = 0.26, PNBC = 0.27, PIND 0.27, PIND = 0.16. Ho: : The proportions are not pPABC Наi РАВС 3 0.31, РсвS 0.26, PNBC 0.16 0.27, 0.16 Но: РАВС 0.31, Рсвs 3D 0.26, Наi РАВС + 0.31, РсвS PNBC + 0.26, PNBC ± 0.27, , PIND + 0.16 Ho: PABC + 0.31, PCBS + 0.26, PNBC + 0.27, PIND + 0.16 0.26, PNBC 0.27, PIND = 0.16 %D На РАВС - 0.31, РсBs 0.26, PNBC 0.27, PIND 0.16 Нo: РАВС - 0.31, РсBS H: The proportions are not PABC 0.16. 0.31,…

The director of library services at a college did a survey of types of books (by subject) in the circulation library. Then she used library records to take a random sample of 888 books checked out last term and classified the books in the sample by subject. The results are shown below. Subject Area Business Humanities. Natural Science Social Science All other subjects USE SALT Percent of Books on Subject in Circulation Library on This Subject 32% 25% 20% 15% 8% Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the distribution of books checked out by students. (a) What is the level of significance? State the null and alternate hypotheses. Ho: The distributions are different. H₁: The distributions are different. H: The distributions are different. H: The distributions are the same. H₁: The distributions are the same. Ho: The distributions are the same. Ho: The distributions are the same. Ho: The distributions are different.…