Bayes’ rule can be used to identify and filter spam emails and text messages. A large collection of real SMS text messagesfrom participating cellphone used in this research. In this collection, 747 of the 5574 total messages (13.40%) are identified as spam.2.The word “free” is contained in 4.75% of all messages, and 3.57% of all messages both contain the word “free” and are marked as spam.a)What is the probability that a message contains the word “free”, given that it is spam?b)What is the probability that a message is spam, given that it contains the word “free”?

6.41 Open source textbook:  A professor using an open source introductory statistics book predicts that 60% of the students will purchase a hard copy of the book, 25% will print it out from the web, and 15% will read it online. At the end of the semester he asks his students to complete a survey where they indicate what format of the book they used. Of the 126 students, 71 said they bought a hard copy of the book, 30 said they printed it out from the web, and 25 said they read it online.(a) State the hypotheses for testing if the professor's predictions were inaccurate. Ho: pBuy = .6, pPrint=.25, pOnline=.15Ha: at least one of the claimed probabilities is different Ho: pBuy = .6, pPrint=.25, pOnline=.15Ha: at least one of the claimed probabilities is zero Ho: pBuy = .6, pPrint=.25, pOnline=.15Ha: all of the claimed probabilities are different Correct   (b) How many students did the professor expect to buy the book, print the book, and read the book exclusively online? (please do not…

6. A study of report writing by psychologist is conducted. A scale that measures the intelligibility of psychologist English is devised. This scale, called an "index of confusion" is devised so that low scores indicate high readability. These data are obtained on articles randomly selected from psychology journals and from unpublished reports written in 2015. Unpublished reports 2.39 Journals 1.79 1.75 1.67 1.65 2.51 2.86 2.14 1.87 1.75 1.94 2.56 2.29 2.49 1.62 2.06 1.33 2.36 2.58 2.33 1.96 1.69 1.70 2.62 2.41 1.94 a. Test the appropriate hypotheses. b. Does there appear to be a difference between u, and u, ? Explain.

If SSWithin = 24.06, SSBetween = 12.33, and there are three groups in the study with 20 cases per group, F = :