A bowl contains seven marbles of which are red while the others are blue. In order

to test the null hypothesis Ho : = 2 against HI : = 4, two of the marbles are

randomly drawn without replacement and the null hypothesis is rejected if and

only if both are red.

(a) What is the probability of committing a Type I error?

(b) What is the probability of committing a Type II error?

a) pr(2 red|theta=2) 2/7x1/6 = 1/21

b) pr(o red, 1 red|theta=4) = 3/7*2/6+4/7*3/6+3/7*4/6=5/7

can some1 explain this to me? i'm a bit lost. i know type 1 error is reject Ho when Ho is actually true.

for for a, i get 2 red marbles. so 2/7 and multiple it 1/6 chance? but why 1/6 chance?

and for b) type2 eror is failing to reject Ho when we actually should. just cant get my head around it some explaination would be great

This is what i got so far

Type I error = "false positive" = rejecting H_0 when H_0 is true

Type II error = "false negative" = accepting H_0 when H_0 is false = accepting H_0 when H_1 is true

So, in symbols:

and

Now you go back and plug in what is meant by reject/accept H_0, and the hypotheses H_0 and H_1 in this problem, to get

and

and then it is just a matter of calculating them, as in the solution.

then, are my numbers correct? just a bit lost in how to interpret the numbers within the question to get the answer.