Question

Draw a sample of 35 plates from a population of 45-lbs plates, where the sample mean found is x=46.5 , where we know the population variance for these plates is o^2=25. What is the confidence interval for the population mean corresponding to a=0.1.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 46.5

Population standard deviation = = 5

Sample size = n = 35

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 * (5 / 35 )

= 2.18

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

- E < < + E

46.5 - 2.18 < < 46.5 + 2.18

43.82 < < 48.68

(43.82 , 48.68)