Question

Construct the confidence interval for the population mean mu. cequals0.90​, x overbar equals 6.8​, sigmaequals0.2​, and nequals59

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 6.8

Population standard deviation = = 0.2

Sample size = n = 59

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (0.2 / 59 )

= 0.043

At 90% confidence interval estimate of the population mean is,

- E < < + E

6.8 - 0.043 < < 6.8 + 0.043

6. 76 < < 6.84

(6.76 , 6.84)