Question

A 98% confidence interval for the average height of the adult American male if a sample of 286 such males have an average height of 59.3 inches with a population deviation of 4.3 inches

round to the nearest hundredth of an inch

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 59.3

Population standard deviation =    = 4.3

Sample size = n =286

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z_/2 = Z_0.01 = 2.326 ( Using z table    )

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

= 2.326 * ( 4.3/  286 )

E= 0.59
At 98% confidence interval estimate of the population mean
is,

- E < < + E

59.3 - 0.59 <   < 59.3+ 0.59

58.71 <   < 59.89

( 58.71 , 59.89 )