Consider the following table in reference to a hypothesis test: Ho True Ho false (1) (3) Accept Ho Reject Ho (2) (4) Before collecting any data, the probability of entry (3) happening is a. 1) True 2) False

Probability will be the basis of all future topics, and you will find that the resulting interpretation of a probability and the |conclusion that you can make from a probability is more important than that calculation itself.Consider the following probabilities found for the given situations, then answer the questions that follow: Situation: If randomly guessing, the probability that a person can correctly guess your BIRTH MONTH on the first try is 1/12= 0.083. You and a friend are out one night and you meet a magician who bets that she can randomly guess both of |1. your BIRTH MONTHS on the first try. QUESTION: If the magician does guess both of your BIRTH MONTHS correctly, would you believe it was by pure chance, or would you believe that the magician knew your BIRTH MONTHS by some other means (whether that be magic, being a creepy stalker, etc.)? Explain your probabilistic and statistical thinking.

A paper demonstrated the application of Bayes's Rule for making inferences about testosterone abuse among athletes. In a population of 1000 athletes, suppose 150 are illegally using testosterone. Of the users, suppose 75 would test positive for testosterone. Of the nonusers, suppose 17 would test positive. a. Given that the athlete is a user, find the probability that a drug test for testosterone will yield a positive result. (This probability represents the sensitivity of the drug test.) (Simplify your answer.)

A biased coin has a 2/3 probability of landing heads and a 1/3 probability of landing tails.You toss the coin 9 times. Which of the two options below is more likely to happen?• The coin lands heads only 3 times, and lands tails 6 times.• The coin lands heads all 9 times.

An experiment can result in one of five equally likely simple events, E₁, E₂, A: E₂, E4 2' P(A) = = 0.4 B: E₁, E3, E4, E5 P(B) = 0.8 C: E₂, E3 Refer to the following probabilities. P(A n B) = 0.2 P(AIB) = 0.25 P(BIA) P(BU C) = 1 P(BIC) 0.5 P(CIB) 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(AUB) (b) P(An B) = 0.5 P(A U B) = ---Select--- + ---Select--- ✓ P(A n B) = ---Select--- (c) P(B n C) Yes P(B n C) = ---Select--- No P(C) = 0.4 . P(B) = = P(C) = = ---Select--- V = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E₁, E₂, E3, E4, E5}) = 1 P(A n B) = P({E₁}) = 0.2 P(B n C) = P({E3}) = 0.2 .., E5. Events A, B, and C are defined as follows.

In the Introduction to Impossibility module, 4/5 of students pass the exam. Of those who pass the exam 9/10 attend lectures, and of those who fail only 1/2 attend lectures. What is the probability that a student who doesn’t attend lectures passes the exam?

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My question for my stats homework comes from the textbook Introduction to the Practice of Statistics Ninth Edition question 4.15  write a sentence about independence before doing the actual problem

The accompanying data are from an article. Each of 309 people who purchased a Honda Civic was classified according to gender and whether the car purchased had a hybrid engine or not. Male Female Hybrid 76 33 Not Hybrid 116 84 Suppose one of these 309 individuals is to be selected at random. Determine if the probabilities P(hybrid male) and P(male hybrid) are equal. If not, explain the difference between these two probabilities. O Yes, the probabilities are equal. No, the probabilities are not equal. The first is the probability that a hybrid Honda Civic owner is male, and the second is the probability that a male Honda Civic owner purchased a hybrid. O No, the probabilities are not equal. The first is the probability that a male Honda Civic owner purchased a hybrid, and the second is the probability that a hybrid Honda Civic owner is male.