Answer to Question #257742 in Statistics and Probability for Manu

Question

Let p be the probability that a coin will fall head in a single toss in order to test Ho : p = 1/2 against H1 : p = 3/4 . The coin is tossed 5 time and Ho is rejected if more than 3 heads obtained. Find the probability of type II error.

Select one: a. 3/8  b. 47/128  c. 9/64  d. 11/24 

Answer 1

The probability of type II error is computed as the probability of not rejecting the null hypothesis given that the true proportion is 0.75.

Therefore the probability of type II error here is computed as:

$= 1 - P(X = 4) - P(X = 5) \\ = 1 - 5 \times 0.75^4 \times 0.25 - 0.75^5 = 0.3672$

Therefore 0.3672 or 47/128 is the required probability here.

Answer: b. 47/128