Question

Suppose we flip a coin 100 times independently and we get 55 heads.
(a) Test H0 : p = 0.5 versus HA : p > 0.5. Report the test statistic and p-value. Make a decision using α = 0.1.
(b) Suppose the decision rule is to reject H0 if ˆp > 0.6. What is the probability of a type I error? If the true value of p is 0.7, then what is the probability of a type II eror?

Answer 1

Goiven data

Number of times coin fliped (n)=100

Number of times head appears =55

Sample propertion

a)Now also given that

Now Test statisc

Now from the Standard probablity distribution table the probablity value for less than Z=1

p(Z<1)=0.8413

Since it is a upper tail test so the probablity value for the given condition will be

p=1-0.8413=0.1587

Now for the Z criticle value

Since Z=1 is less than Criticle value of Z =1.282 so we can say that we dont have enough evidence to reject the null hypothesis

b) Here given that

Sample propertion

Now Test statisc

probablity of tipe 1 error

p=1-0.9772=0.0228

now given that

p=0.7

so the test static will be like

probablity of type two error will be

p=1-0.0146=0.9854