Question

99% confidence interval will be more accurate than a 95% confidence interval based on the same sample size, it will be less precise because it will be wider than a 95% confidence interval.

1. what is your favorite thing about the season of fall? a researcher surveys a random sample consisting of ( n = 725 ) adults and finds that 382 of these adults say the best thing about the fall season is cooler weather. from this information, calculate the sample proportion below and round your answer to exactly three decimal places.

Explanation:

Step1: Recall the formula for sample proportion

The formula for sample proportion $\hat{p}$ is $\hat{p}=\frac{x}{n}$, where $x$ is the number of successes in the sample and $n$ is the sample size.

Step2: Identify the values of $x$ and $n$

Here, $x = 382$ (number of adults who say the best thing about fall is cooler weather) and $n=725$ (total number of adults surveyed).

Step3: Calculate the sample proportion

Substitute the values into the formula: $\hat{p}=\frac{382}{725}$.
Using a calculator, $\frac{382}{725}=0.5268965517$.

Step4: Round the result

Rounding $0.5268965517$ to three decimal places. Looking at the fourth decimal place (8), we round up the third decimal place. So, $0.527$.

Answer:

$0.527$