Question

1. A random sample of 81 observations produced a mean value of 89 and standard deviation of 5.5. The 95% confidence interval for the population mean μ is between?

a) 88.302 and 89.698
b) 87.302 and 90.698
c) 85.802 and 91.198
d) 87.995 and 90.005
e) 87.802 and 90.198

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 89

Population standard deviation =    = 5.5

Sample size n =81

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* ( 5.5/ 81 )

= 1.298
At 95% confidence interval estimate of the population mean
is,

- E < < + E

89 - 1.298 <   < 89 + 1.298

c) 85.802 and 91.198 APPROXIMATELY