Question

The average commute times for employees of a large company is 32 minutes. The commute time of 10employees are 40, 31, 32, 16, 25, 35, 22, 53, 23, and 33.a) Determine the sample mean and the population mean.b) What is the estimated margin oferror of the sample population, using standard deviation (round to thetenths place)?

Answer 1

Given:

40,31,32,16,25,35,22,53,23 and 33.

a)

Sample mean:

$\bar{x}=32$

Population mean:

$\mu=\frac{\Sigma(x_i)}{n}_{}$$\mu=\frac{40+31+32+16+25+35+22+53+23+33}{10}$$\mu=\frac{310}{10}$$\mu=31$

b)

$\sigma=\sqrt[]{\frac{\Sigma(x-\mu)^2}{n-1}}$$\sigma=\sqrt[]{\frac{81+0+1+225+36+16+81+484+64+4}{10-1}}$$\sigma=\sqrt[]{\frac{992}{9}}$$\sigma=\frac{\sqrt[]{992}}{3}$$\sigma=10.4987$$\text{Error}=\pm z\times\frac{\sigma}{\sqrt[]{n}}$

z value is not given so taken as 95% on confidence level

$z=1.96$$\text{Error}=\pm1.96\times\frac{10.4987}{\sqrt[]{10}}$$\text{Error}=\pm6.5072$$\text{Error}=\pm6.5$