Question

In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home. Give the value of the standard error for the point estimate.

Answer 1

Answer:

The value of the standard error for the point estimate is of 0.0392.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home.

This means that $n = 100, p = \frac{81}{100} = 0.81$

Give the value of the standard error for the point estimate.

This is s. So

$s = \sqrt{\frac{0.81*0.19}{100}} = 0.0392$

The value of the standard error for the point estimate is of 0.0392.