Question

A survey was given to a random sample of 45 voters in the United States to ask about

their preference for a presidential candidate. Of those surveyed, 80% of the people
said they preferred Candidate A. Determine a 95% confidence interval for the
percentage of people who prefer Candidate A, rounding values to the nearest tenth.

Answer 1

Answer: A confidence interval is a range of values that is likely to contain the true population value with a certain level of confidence. To determine a 95% confidence interval for the percentage of people who prefer Candidate A, we can use the following formula:

(Sample proportion) +/- (Margin of error)

The margin of error can be calculated using the formula:

Margin of error = (Critical value) * (Standard deviation)

The critical value is a factor used to compute the margin of error. The critical value for a 95% confidence interval is approximately 1.96. The standard deviation is calculated as:

Standard deviation = √((Sample proportion) * (1 - Sample proportion) / (Sample size))

Plugging in the given values:

Sample proportion = 80% = 0.8

Sample size = 45

Margin of error = (1.96) * √((0.8) * (1 - 0.8) / (45))

Explanation: