Question

vegans are much less common in the united states than in the rest of the world. suppose in a 2018 survey of 12,000 people in the united states, veganbits found 60 who are vegans. (a) develop a point estimate of the proportion of people in the united states who are vegans. 0.005 correct: your answer is correct. (b) set up a hypothesis test so that the rejection of h0 will allow you to conclude that the proportion of people in the united states who are vegans exceeds 0.004. (enter !

Answer 1

The point estimate for the proportion of vegans in the United States is 0.005, or 0.5%. For a hypothesis test aiming to conclude that the proportion exceeds 0.004, the null hypothesis (H0) would be that the proportion p is less than or equal to 0.004, and the alternative hypothesis (Ha) would be that p is greater than 0.004.

Step-by-step explanation:

To answer the student's questions, we will first address part (a) by calculating a point estimate of the proportion of vegans in the United States and then set up a hypothesis test for part (b).

Part A: Point Estimate of Proportion

The point estimate for the proportion of vegans in the United States can be found by dividing the number of vegans by the total number of people surveyed:

Point Estimate = Number of Vegans / Total Number Surveyed

Point Estimate = 60 / 12,000 = 0.005

This means the point estimate of the proportion of people in the United States who are vegans is 0.005, or 0.5%.

Part B: Hypothesis Test Setup

Next, for the hypothesis test we want to test if the true proportion of vegans in the United States exceeds 0.004. The hypotheses can be set up as follows:

H0: p ≤ 0.004 (Null Hypothesis: The proportion of vegans is less than or equal to 0.004)

Ha: p > 0.004 (Alternative Hypothesis: The proportion of vegans is greater than 0.004)

In this hypothesis test, we are looking for evidence to reject the null hypothesis in favor of the alternative hypothesis, which would suggest that the proportion of vegans is indeed greater than 0.004.