Question

The average per capita spending on health care in the Canada is $5170 based on the sample of 70 individuals. The standard deviation is $687 and the distribution of health care spending is approximately normal. Find the best point estimate of the population mean and the 99% confidence interval of the population mean.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 5170

Population standard deviation =    = 687

Sample size = n = 70

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576   ( Using z table )

Margin of error = E = Z_/2* ( /n)

= 2.576 * ( 687/ 70)

= 211.52

At 99% confidence interval estimate of the population mean is,

- E < < + E

5170- 211.52 < < 5170+211.52

4958.48 , 5381.52

best point estimate of the population mean and the 99% confidence interval of the population mean.

Point estimate = sample mean = = 5170