Question

According to a Yale University poll conducted in December 2018, 70% of U.S. adults think that global warming is happening. If this is true, what is the probability that a random sample of 525 U.S. adults will estimate this parameter within ± 3 percentage points?

Answer 1

The probability that a random sample of 525 U.S. adults will estimate the parameter within ± 3 percentage points is approximately 90.98%

Step-by-step explanation:

To determine the probability that a random sample of 525 U.S. adults will estimate the parameter within ± 3 percentage points, we need to calculate the margin of error.

Margion of error = (Z-value) * (Standard deviation)

To calculate the Z-value, we need to determine the confidence level. Let's assume a 95% confidence level, which corresponds to a Z-value of 1.96.

With a 70% estimate of U.S. adults thinking that global warming is happening, the standard deviation can be calculated as follows:

Standard deviation = sqrt((p * (1 - p)) / n)

Standard deviation = sqrt((0.70 * 0.30) / 525)

Standard deviation ≈ 0.023

Now, we can calculate the margin of error:

Margin of error = (1.96) * (0.023)

Margin of error ≈ 0.0451

Finally, to calculate the probability that the sample estimate will be within ± 3 percentage points, we consider the margin of error as the range:

Probability ≈ 1 - (2 * margin of error)

Probability ≈ 1 - (2 * 0.0451)

Probability ≈ 0.9098 or 90.98%