Please do questions 3,4,5 pbinom (2,size=10,prob=D0.3)## [1] 0.3827828 Consider a random sample X1,...,Xn of voters who either voted for Candidate A (“X; =1") or for Candidate B (“X; = 0"). Denote the probability of voting for Candidate A by p.We wish to testHo : p 2 0.5 vs. Hị : p< 0.5.(i.e. the hypothesis that Candidate A will not loose the election).(1) Consider a test of the above hypothesis of the formi=1for some integer c. Calculate the power of this test and show that it is a decreasingfunction of p for any c e {0, ...,n – 1}.(2) Suppose that n = 20. Find c so that ý in (1) is a test at level 10% with the largestpossible power (from among the tests of the same form at level 10%). What is the sizeof your test? Use that the CDF of the binomial distribution with size 20 and successprobability 0.5 evaluated at z = 0,..., 20 equals (rounded to 3 decimal places)round (pbinom(0:20, size=20,p=0.5),3)##[1] 0.000 0.000 0.000 0.001 0.006 0.021 0.058 0.132 0.252 0.412 0.588 0.748## [13] 0.868 0.942 0.979 0.994 0.999 1.000 1.000 1.000 1.000(3) Suppose that 5 voters voted for candidate A and 15 for candidate B. Is it safe toconclude using the test you derived in part (2) at level 10% that candidate A willloose the election?(4) Suppose that 15 voters voted for candidate A and 5 for candidate B. Is it safe toconclude using the test you derived in part (2) at level 10% that candidate A willnot loose the election?For the test that you derived in part (2) (again with(5)n = 20), calculate the propăbility of type II error when p = 0.4.You are allowed and encouraged to use software to calculate binomial probabilities.In R, the CDF F(x) of the binomial distribution with size n and success probabilityp can be calculated as follows: For example, for x = 2, n = 10 and p = 0.3 we get

From the given information, H0:p≥0.5 vs. H1:p<0.5 Let X1,X2,...,Xn of voters who either voted for…

(3) Suppose that 5 voters voted for candidate A and 15 for candidate B. Is it safe to conclude using the test you derived in part (2) at level 10% that candidate A will loose the election? (4) Suppose that 15 voters voted for candidate A and 5 for candidate B. Is it safe to conclude using the test you derived in part (2) at level 10% that candidate A will

(3) Suppose that 5 voters voted for candidate A and 15 for candidate B. Is it safe to conclude using the test you derived in part (2) at level 10% that candidate A will loose the election? (4) Suppose that 15 voters voted for candidate A and 5 for candidate B. Is it safe to conclude using the test you derived in part (2) at level 10% that candidate A will

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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