Suppose we are interested in testing whether a coin is fair based on the number of heads, Y, in 20 tosses of the coin. Let p denote the true probability of getting heads on a single toss of the coin.
Then we wish to test H_(0):p=0.5 against H_(a):p=0.5.
We will use a rejection region of the form RR={Y:|Y-10|>=4} - so H_(0) is rejected if Y<=6 or Y>=14. Use the table of cumulative binomial probabilities to help answer the following:
(a) Calculate the significance level, alpha , of the test.
(b) Determine eta , the probability of a type II error, if p=0.6.
(c) Determine eta , the probability of a type II error, if p=0.7.
(d) Determine eta , the probability of a type II error, if p=0.8.
(e) Find the smallest value of c such that a rejection region of the form RR={Y:|Y-10|>=c} will result in a significance level of at most 0.01 .
Show all work please.
1. Suppose we are interested in testing whether a coin is fair based on the number of heads,Y, in 2o tosses of the coin. Let p denote the true probability of getting heads on a single toss of the coin Then we wish to test Hop =0.5 against Ha:p=0.5. We will use a rejection region of the form RR={Y|Y-10|4}-so Ho is rejected if Y6 or Y14.Use the table of cumulative binomial probabilities to help answer the following: (a) Calculate the significance level, a, of the test. (b) Determine ,the probability of a type II error,if p=0.6. (c) Determine ,the probability of a type II error,if p =0.7. (d) Determine ,the probability of a type II error,if p =0.8. (e) Find the smallest value of c such that a rejection region of the form RR={Y:|Y-10| c} will result in a significance level of at most 0.01.