Please expline the Furmula that you use it and what R studio commond we can used
ID: 3021042 • Letter: P
Question
Please expline the Furmula that you use it and what R studio commond we can used to find right Answer. No SIM 3:43 PM 193% Home Insert Layout ReviewView Calibri 3) A multiple-choice quiz contains ten questions. For each question there are one correct answer and A student gets three correct answers on the quiz. Test the hypothesis that the four incorrect answers. student is guessing, against the alternative that his probability of a correct answer is higher than fora random guesser Ho: p vs H.: p ..(You need one number, and one inequality sign). PB3] (the subscript p is your answer on the previous line) Suppose that if a student gets 4 or more questions correct, the hypothesis that a student is a “guesser" is rejected. What is the power of this test for a student who has the following probability for a correct answer on each question: p- 4, power p.5, power p6, power 4) In an experiment to test if a subject has ESP (Extra Sensory Perception), the tester selects a card at random from a set of 4, each of which has a picture of a shape (circle, square, triangle, or star). The tester concentrates on a shape, and the subject tries to guess which shape it is. This is repeated n 100 times. Let B be the number of correct guesses for a "pure guesser" (no ESP). Find E B] Suppose it is decided to reject the null hypothesis that the subject is a guesser if he/she gets at least 35 out of 100 correct. Find the power of this test if p, the probability of a correct guess for the subject is: p=.25, power---' p-.35, power ; p-.45, power-_-; Note: the subject knows what the four shapes are, but not which one was selected on each trial)
Explanation / Answer
3) n =10 x=no of correct answers = 3 p for guessing right 0.20 q for notright 0.8 X is binomial H0: p=0.2 vs Ha:p>0.2 Student p 0.3 p diff 0.1 std error 0.126491 t 0.790569 df 9 p value 0.232397 Since p >0.05 accept null hypothesis, i.e. mere guessing Case II p >=0.4 p diff 0.2 t 1.581139 df 9 p value 0.074282 power of test =0.80 4) n=100 p=0.25 E(B) =np=25 Var npq 18.75 std dev 4.330127