Question

Salaries of

42

college graduates who took a statistics course in college have a​ mean,

x overbarx​,

of

$ 63 comma 63,300.

Assuming a standard​ deviation,

sigmaσ​,

of

​ 15,697​,

construct a

95​%

confidence interval for estimating the population mean

muμ.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 63300

Population standard deviation =    = 15697

Sample size n =42

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* ( 15697/ 42 )

= 4747.3154
At 95% confidence interval estimate of the population mean
is,

- E < < + E

63300 - 4747.3154 <   < 63300+ 4747.3154

58552.6846 <   < 68047.3154
( 58552.6846 , 68047.3154 )