In an experiment with N = 14 and P _real = 0.10, what is the power using a = 0.05_{2 tail}? A) 0.8417 B) 0.0132 C) 0.0000 D) 0.0500

Question

Quizplus · Accepted Answer

To find the power, we need to first calculate the probability of rejecting the null hypothesis when it is actually false (i.e. the probability of obtaining a significant result).

Under the alternative hypothesis, P = 0.10 (given in the question).

The null hypothesis states that P = 0.05, so we can use a binomial distribution to calculate the probability of observing a certain number of successes (i.e. number of individuals with the outcome of interest) in a sample of size N.

The critical value for rejecting the null hypothesis at a significance level of a = 0.05 with a two-tailed test is 1.96 (using a standard normal distribution).

Therefore, the power is the probability of observing a result that falls into the rejection region (i.e. greater than 1.96 or less than -1.96) when the true probability is 0.10.

We can calculate this using the formula for a binomial distribution:
power = 1 - (P(X<=1.96) + P(X>=-1.96))
where X ~ B(14, 0.10).

Using a binomial calculator or a statistical software, we get:
power = 0.8417

Therefore, the best choice is A, as it gives the correct power calculation.

In an Experiment with N = 14 and P real

In an Experiment with N = 14 and P _real