Data associated with gold daily price per gram during the last five years indicates a distribution with mean $32.52 and standard deviation $7.42. What is the standard deviation of $ \bar{x}$ when it is based on a random sample of size n = 196?
A) 0.04
B) 2.32
C) 0.01
D) 0.53

Question

Data associated with gold daily price per gram during the last five years indicates a distribution with mean $32.52 and standard deviation $7.42. What is the standard deviation of $  \bar{x}$ when it is based on a random sample of size n = 196?
A) 0.04
B) 2.32
C) 0.01
D) 0.53

Quizplus · Accepted Answer

The standard deviation of the sample mean $ \bar{x} $ is calculated using the formula $ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} $, where $ \sigma $ is the population standard deviation and $ n $ is the sample size. Here, $ \sigma = 7.42 $ and $ n = 196 $, so $ \sigma_{\bar{x}} = \frac{7.42}{\sqrt{196}} = \frac{7.42}{14} = 0.53 $.

Data Associated with Gold Daily Price Per Gram During the Last