Question

Exercise 8-2 A sample of 43 observations is taken from a normal population with a standard deviation of 24. The sample mean is 43. Determine the 80% confidence interval for the population mean. (Round the final answers to 3 decimal places.) Confidence interval for the population mean is and .

statistics

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 43

Population standard deviation =    = 24

Sample size n =43

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z/2 = Z0.10= 1.28 ( Using z table )

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

= 1.28 * (24 /  43 )

= 4.685
At 80% confidence interval estimate of the population mean
is,

- E < < + E

43 - 4.685 <   <43 + 4.685

38.315 <   < 47.685

( 38.315 47.685 )