PROBLEM 7 An editor has a stack of k documents to review. The order in which the doc- uments are reviewed is random with cach ordering being equally likely. Of the k documents to review, two are named "Relaxation Through Mathematics" and "The Joy of Calculus." Give an expression for cach of the probabilities below as a function of k. Simplify your final expression as much as possible so that your answer does not include any expressions in the form ()- (a) What is the probability that “Relaxation Through Mathematies" is first to review? (b) What is the probability that “Relaxation Through Mathematics" and "The Joy of Calculus" are next to each other in the stack?

If variances are unequal, you pool the variances Typed answer will be automatically saved. X, X S2- Write your response here...

We are interested in looking at the effect of a baseball player’s free agent status on their salary. We look at 337 baseball players and categorize them as either having a high salary (above 2 million) or not, and as either being free agents or not. ------------------------------------- You also wonder if having a high batting average affects the salary of baseball players. You classify all 370 baseball players as having a high batting average if it is over .300. 1. What are the variables you are looking at? What are the possible categories within each variable? Which is the explanatory, and which is the response? 2. If we want to perform a χ2 test to see if there is a relationship between the two variables, what is our null and alternative hypothesis?

A certain affects virus 0.8% of the population. A test used to detect the virus in a person is positive 88% of the time if the person has the virus (true positive) and 13% of the time if the person does not have the virus (false postive). Fill out the remainder of the following table and use it to answer the two questions below.  (enter answer with no commas, i.e. as 1000 not 1,000.)     Infected Not Infected Total Positive Test [a] [b] [c] Negative Test [d] [e] [f] Total 800 99,200 100,000 i) Find the probability that a person has the virus given that they have tested positive. (Round your answer to the nearest tenth of a percent and do not include a percent sign.)[g]_______ % ii) Find the probability that a person does not have the virus given that they test negative. (Round your answer to the nearest tenth of a percent and do not include a percent sign.)[h]________ %

Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 5. You are playing Scrabble and you draw seven tiles: M, A, T, C, H, E, S. You line them up in some random order on your tile rack (assume all orderings are equally likely). The events M, T, and S are defined as follows: M: The tiles M, A, T, H appear consecutively. T: The tile T appears exactly in the middle (fourth position). S: The tile S is either in the first position or in the final position. Calculate the probability of each event; that is, p(M), p(T), and p(S). 5.1 5.2 What is p(MIT)? 5.3 What is p(MIS)? 5.4 5.5 What is p(T|S)? Consider all pairs of events: (M,T), (M,S), and (T,S). Which pairs of events are independent and which pairs of events are not independent? Justify your answer.

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The population mean annual salary for environmental compliance specialists is about ​$63 comma 00063,000. A random sample of 3131 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than ​$59 comma 00059,000​? Assume sigmaσequals=​$5 comma 8005,800. (Need help solving this)

Choose all of the following true statements. {7,"Albert R.", 7/2, True} is not a set because it contains mixed data types. {7,"Albert R.", T/2, True} is a set. {7,"Albert R.", T/2, True} is the same as {True, "Albert R.", 7, 7/2} O 14/2 e {7," Albert R.", 7/2, True} O T/3 € {7,"Albert R.", 7/2, True} O 2/3 ¢ Z ACB= Vx. [x E A → x E B where A, B are sets. 6. {3} € {5,7,3} The empty set is a subset of every set.

A researcher is interested in the reaction time of college students under high cognitive load. The students are asked to remember a random number sequence. While trying to remember the number sequence, the students are instructed to press the space key after they hear a tone on the computer. The researcher measures the time between when the tone occurs and when the space key is pressed. The variable being measured is a ___________ variable.

(For Questions 17-19 and 20-24). The following data was collected from a clinical trial testing a new drug aimed to lower blood pressure for individuals older than age 45. Half of the 20 participants received the new drug (Treatment = Yes) and the other half of the participants received a placebo pill (Treatment = No). Their age and gender was also recorded. Please use this data for Questions 17-19 and 20-24 and note, not all the information in the table will be used for either problem, you must decide what is relevant based on what the problem is asking. Subject ID Treatment Age Gender BP_Before BP_After D1 Yes 65 F 103.3 80.5 D2 Yes 59 F 93.6 85.9 D3 Yes 60 M 92 85.2 D4 Yes 54 F 93 87.8 D5 Yes 65 F 95.4 85.3 D6 Yes 57 M 109.6 94.2 D7 Yes 69 M 97.9 83.9 D8 Yes 62 M 96 85 D9 Yes 49 F 98.4 86.3 D10 Yes 45 M 98.4 90 C1 No 63 F…