Final answer:
To construct a 95% confidence interval for the proportion of adults in the United States who are vegetarians, calculate the point estimate and error bound and use them to calculate the lower and upper bounds.
Step-by-step explanation:
To construct a 95% confidence interval for the proportion of adults in the United States who are vegetarians, we first need to calculate the point estimate and the error bound.
The point estimate is the proportion of vegetarians in the sample, which is 47/1021 = 0.046, or 0.046 as a decimal. The error bound can be calculated using the formula z * sqrt((p(1-p))/n), where z is the z-value for the desired confidence level (1.96 for a 95% confidence level), p is the point estimate, and n is the sample size. With the given values, the error bound is approximately 0.016.
The confidence interval is then calculated by subtracting the error bound from the point estimate to get the lower bound, and adding the error bound to the point estimate to get the upper bound. So, the 95% confidence interval for the proportion of adults in the United States who are vegetarians is 0.046 - 0.016 to 0.046 + 0.016, or 0.030 to 0.062.