Question

The following population is provided:17, 15, 8, 9, 7, 9, 11, 12, 14, 16, 9, 5, 10, 14, 13, 12, 12, 11, 9, 14, 8, 14, 12. Further, a simple random sample from this population gives the following values: 12, 9, 5, 10, 14, 11. Compute the sampling error for the sample mean.

a. 1.811 b. 1.167 c. 1.181 d. 1.348 e. None of the above

Answer 1

The sampling error for the sample mean is

$$\sigma_{\bar{x}}=\sqrt{\dfrac{\sigma^2}{n}}$$

$$\mu=\dfrac{1}{23}(17+15+8+9+7+9$$

$$+11+12+14+16+9+ 5+10$$

$$+14+13+12+12+11+9+ 14$$

$$+8+14+12)=\dfrac{261}{23}$$

$$\sigma^2=\dfrac{\Sigma_i(x_i-\mu)^2}{N}=\dfrac{205.21739130435}{23}$$

$$\sigma_{\bar{x}}=\sqrt{\dfrac{\sigma^2}{n}}$$

$$=\sqrt{\dfrac{205.21739130435}{23(6)}}=1.219$$

e. None of the above