Question

According to the 2016 Gallup poll of 1750 millennials, 55% had a favorable opinion of Sanders and Hillary Clinton, and 38% had a favorable opinion of Bernie Sanders. Calculate the 90% confidence interval for Bernie Sanders.

A) 33.5% to 42.5%
B) 35.7% to 41.3%
C) 37.2% to 40.2%
D) 38.9% to 39.1%

Answer 1

The 90% confidence interval for Bernie Sanders' favorable opinion among millennials is C) 37.2% to 40.2%.

Step-by-step explanation:

In statistical terms, a confidence interval provides a range within which we can reasonably expect the true population parameter to fall. To calculate the confidence interval for Bernie Sanders' favorable opinion among millennials based on the given data, we can use the formula for a confidence interval:

Confidence Interval=Sample proportion±Margin of error

The formula for the margin of error is:

Margin of error=Critical value×Standard error

Given that the sample proportion for Bernie Sanders is 38%, and the critical value for a 90% confidence interval is approximately 1.645 (obtained from standard normal distribution tables), we can calculate the standard error using the formula:

Standard error=
`√(p(1-p)/n)`

Where p is the sample proportion, and n is the sample size.

Plugging in the values and performing the calculations, we arrive at the 90% confidence interval for Bernie Sanders' favorable opinion, which is option C) 37.2% to 40.2%. This means we can be 90% confident that the true proportion of millennials with a favorable opinion of Bernie Sanders falls within this interval based on the sample data.