In: Statistics and Probability
Suppose a sample has a sample mean of 53, a sample size of 40, and the population has a standard deviation of 4. We want to calculate a 99% confidence interval for the population mean. The critical Z* in this case is 2.576. The confidence interval is (to one decimal place),
a. (42.7, 63.3)
b. (48.8, 57.2)
c. (49, 57)
d. (51.4, 54.6)
e. (52.4, 53.6)
f. (52.7, 53.3)
Solution :
Given that,
= 53
= 4
n = 40
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576
Margin of error = E = Z/2* (/n)
= 2.576 * (4 / 40 )
= 1.6
At 99% confidence interval estimate of the population mean is,
- E < < + E
53 - 1.6 < < 53 + 1.6
51.4 < < 54.6
(51.4, 54.6)
Option d ) is correct.