Question

A recent poll reported that Dr. Anthony Fauci's approval rating is at 54% with a confidence level of 95% and a standard error of ‡3%.Give the confidence interval.

Answer 1

To compute the confidence interval, we need to determine the range within which we are 95% confident the true percentage of people who approve of Dr. Anthony Fauci falls. The confidence interval can be calculated by adding and subtracting the product of the standard error and the critical value from the mean.

Step-by-step explanation:

To compute the confidence interval, we need to determine the range within which we are 95% confident the true percentage of people who approve of Dr. Anthony Fauci falls. The confidence interval can be calculated by adding and subtracting the product of the standard error and the critical value from the mean.

In this case, since the approval rating is 54% and the standard error is ‡3%, we can calculate the confidence interval as follows:

Confidence Interval = 54% ± (3% * Critical Value)

Given that the confidence level is 95%, the critical value can be found using a standard normal distribution table. The critical value for a 95% confidence level is approximately 1.96.

Therefore, the confidence interval is 54% ± (3% * 1.96), which simplifies to 54% ± 5.88%. This means we are 95% confident that the true approval rating for Dr. Anthony Fauci falls between 48.12% and 59.88%.