Question

Suppose that you are interested in determining the average height of a person in a large city. You begin by collecting the heights of a random sample of 196 people from the city. The average height of your sample is 68 inches, while the standard deviation of the heights in your sample is 7 inches. The standard error of your estimate of the average height in the city is

Answer 1

Answer:

The standard error of your estimate of the average height in the city is 0.5 inches.

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.

You begin by collecting the heights of a random sample of 196 people from the city.

This means that $n = 196$

The standard deviation of the heights in your sample is 7 inches.

This means that $\sigma = 7$

The standard error of your estimate of the average height in the city is

$s = \frac{\sigma}{\sqrt{n}} = \frac{7}{\sqrt{196}} = 0.5$

The standard error of your estimate of the average height in the city is 0.5 inches.