Question

If Upper X overbar equals71​, sigma equals 14​, and n equals 66​, construct a 99% confidence interval estimate of the population​ mean, mu .

_ < or equal mu < or equal _

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 71

Population standard deviation =    = 14
Sample size = n =66

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   ( Using z table )

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

= 2.576 * ( 14/ 66)

= 4.44

At 99% confidence interval mean is,

- E < < + E

71-4.44 < < 71+4.44

66.56< < 75.44