in a random sample of 56 people, 28 are classified as \successful.\ a. determine the sample proportion, p…

in a random sample of 56 people, 28 are classified as \successful.\ a. determine the sample proportion, p, of \successful\ people. b. if the population proportion is 0.65, determine the standard error of the proportion. a. p = 0.50 (round to two decimal places as needed.) b. $sigma_p=square$ (round to four decimal places as needed.)

in a random sample of 56 people, 28 are classified as \successful.\ a. determine the sample proportion, p, of \successful\ people. b. if the population proportion is 0.65, determine the standard error of the proportion. a. p = 0.50 (round to two decimal places as needed.) b. $sigma_p=square$ (round to four decimal places as needed.)

Answer

Explanation:

Step1: Recall standard - error formula

The formula for the standard error of a proportion is $\sigma_p=\sqrt{\frac{p(1 - p)}{n}}$, where $p$ is the population proportion and $n$ is the sample size.

Step2: Identify values

We are given that $p = 0.65$ and $n=56$.

Step3: Substitute values into formula

$\sigma_p=\sqrt{\frac{0.65\times(1 - 0.65)}{56}}=\sqrt{\frac{0.65\times0.35}{56}}$. First, calculate $0.65\times0.35 = 0.2275$. Then, $\frac{0.2275}{56}\approx0.0040625$. Finally, $\sigma_p=\sqrt{0.0040625}\approx0.0638$.

Answer:

$0.0638$