Consider the following to answer the question(s) below:
According to a recent survey, about 33% of Canadians polled said that they would likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed at a local supermarket.
-Which of the following statements is (are) true about the sampling distribution of the sample proportion?
A) The sampling distribution can be described by the Normal model.
B) The mean of the sampling distribution is 0.33.
C) The standard deviation of the sampling distribution is 0.07.
D) All of the above
E) None of the above

Question

Quizplus · Accepted Answer

Since the sample size n = 45 is large enough (greater than or equal to 10), the sampling distribution of the sample proportion can be approximated by the Normal model. The mean of the sampling distribution is equal to the population proportion, which is given as 0.33. The standard deviation of the sampling distribution can be calculated as 
sqrt[(p*q)/n] where p = 0.33, q = 0.67, and n = 45. Plugging in these values, we get sqrt[(0.33*0.67)/45] ≈ 0.07. Therefore, all the statements A, B, and C are true, and the correct choice is D.

Consider the Following to Answer the Question(s) Below