A dietitian wants to know the average number of vegetarians in his State. He would like to obtain the data with the margin of error no more than 0.01 for the confidence level of 95%. According to his previous studies, he knows that the population proportion of vegetarians is approximately 3.2%. Four hundred people took part in the previously studied. Should the dietitian invite the same number of people for the new study to obtain the margin of error no more than 0.01?
A)The dietitian can invite 400 people for this study.
B)The dietitian needs to take more than 400 people for this study.
C)The dietitian can take less than 400 people, but more than 310 people.
D)We need more information to answer the question.

Question

Quizplus · Accepted Answer

The margin of error (ME) in a proportion is calculated using the formula ME = Z * sqrt[(p(1-p))/n], where Z is the Z-score corresponding to the confidence level (for 95%, Z ≈ 1.96), p is the population proportion, and n is the sample size. Given a desired ME of 0.01, p = 0.032, and solving for n would show that the required sample size is greater than 400 to achieve the desired margin of error.

A Dietitian Wants to Know the Average Number of Vegetarians