Question

When a population is finite, the formula that determines the standard error of the mean o- needs to be adjusted. If N is the size of the population and n is the size of the N -n N -n sample (where n 20.05N), then the standard error of the mean is 0-=- .. The expression H i s called the finite population correction factor. Use the V N -1 finite population correction factor to construct the confidence interval for the population mean described below. N -1 c=0.80 X = 65.6 o= 1.7 N=600 n=81 D. The 80% confidence interval for the population mean is ( (Round to two decimal places as needed.)

Answer 1

Standard error

$\small \sigma_{\overline{x}} = \frac{1.7}{81}\sqrt{\frac{600-81}{600-1}}$

$\small \sigma_{\overline{x}} =0.0195$

For 80% confidence, z = 1.28

Hence,

80% confidence interval will be:

(65.6 - 1.28*0.0195, 65.6 + 1.28*0.0195)

(65.58, 65.62)