Question

Suppose 13% of American adults believe that the highest priority of America is to protect freedom of speech. We will take a random sample of 2 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is___________.a. approximately Normal, with mean .b. 13 and standard error .c. 238 approximately Normal, with unknown mean and standard deviation. d. Binomial, with n=2 and p=.13. e. neither Normal, not Binomial.

Answer 1

Then the sampling distribution of the sample proportion of people who answer yes to the question is d. Binomial, with n=2 and p=.13

Explanation:

Here, we are given a probability that 13% of American adults believe that the highest priority of America is to protect freedom of speech, which means, if we ask this question to a sample of American adults, they will answer 'yes' with a probability of p=0.13 and 'no' with a probability of q = 1=p = 1 - 0.13 = 0.87. So, we can say that there are 2 outcomes, either yes or no, each with probabilities p and q, respectively.

Hence, this is a binomial distribution with n=2 and p=0.13. Where n is the total number of people who answered the question and p is the probability of them answering 'yes'. d is the correct option.