Question

Let p be the probability that a coin will fall head in a single toss in order to test the null
hypothesis 0: = 1/2 against the alternate hypothesis 1: = 3/4. The coin is tossed 5
times and 0 is rejected if more than 3 heads are obtained. Determine the probability of
type I and type II errors.

Answer 1

Answer:

In hypothesis testing a decision between two alternatives, one of which is called the null hypothesis and the other the alternative hypothesis, must be made. As an example, suppose you are asked to decide whether a coin is fair or biased in favor of heads. In this situation the statement that the coin is fair is the null hypothesis while the statement that the coin is biased in favor of heads is the alternative hypothesis. To make the decision an experiment is performed. For example, the experiment might consist of tossing the coin 10 times, and on the basis of the 10 coin outcomes, you would make a decision either to accept the null hypothesis or reject the null hypothesis (and therefore accept the alternative hypothesis). So, in hypothesis testing acceptance or rejection of the null hypothesis can be based on a decision rule. As an example of a decision rule, you might decide to reject the null hypothesis and accept the alternative hypothesis if 8 or more heads occur in 10 tosses of the coin.

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