Question

X-bar 12.48, Standard deviation of a population 7.8, Confidence internal 95%, Sample size 50 ......(From all adults that live in New York city , 50 of them had id cards).

Construct a 99% confidence interval for the mean of your population using your sample data. Clearly explain how you arrived at your sample data. Clearly explain ho you arrived at your interval, including any critical values that you used and the error amount in your interval. Identify your sample information and the error amount .

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 12.48

Population standard deviation = = 7.8

Sample size = n = 50

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (7.8 / 50)

= 2.2

At 95% confidence interval estimate of the population mean is,

- E < < + E

12.48 - 2.2 < < 12.48 + 2.2

10.28 < < 14.68

(10.28 , 14.68)