Question

Construct a 98% confidence interval when n = 20, x = 67.5 and σ = 3.7.

Answer 1

Solution :

Given that,

Point estimate = sample mean =   =67.5

Population standard deviation =    = 3.7

Sample size = n =20

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

Margin of error = E = Z/2    * ( /n)

= 2.326 * ( 3.7/  20 )

= 1.92
At 98% confidence interval estimate of the population mean
is,

- E < < + E

67.5 - 1.92 <   < 67.5+ 1.92

65.58 <   < 69.42

( 65.58, 69.42 )