Question

ch 20 the estimate s introduces additional variation into the t statistic, so the t distribution is _________ spread out than the standard normal distribution. no more more less question 5 1 pts ch 20 a study of commuting times reports the travel times to work of a random sample of 500 employed adults. the mean is \\( \overline { x } = 50 \\) minutes and the standard deviation is \\( s = 45 \\) minutes. what is the standard deviation of the mean? 50 / 45 45 / \\( \sqrt { 500 } \\) 50 / \\( \sqrt { 500 } \\) 45 / 500

Explanation:

Step1: Recall the formula for the standard deviation of the mean

The formula for the standard deviation of the mean (also known as the standard error) is \( \sigma_{\bar{x}}=\frac{s}{\sqrt{n}} \), where \( s \) is the sample standard deviation and \( n \) is the sample size.

Step2: Identify the values of \( s \) and \( n \)

Given that \( s = 45 \) minutes (sample standard deviation) and \( n=500 \) (sample size).

Step3: Substitute the values into the formula

Substituting \( s = 45 \) and \( n = 500 \) into the formula \( \sigma_{\bar{x}}=\frac{s}{\sqrt{n}} \), we get \( \sigma_{\bar{x}}=\frac{45}{\sqrt{500}} \).

Answer:

\( 45/\sqrt{500} \)