Question

a random sample of 64 observations produced a mean value of 84 and standard deviation of 4.5 the 95% confidence interval for the population mean u is between

a. 80.898 and 87.103

b. 82.398 and 85.603

c. 83.075 and 84.925

d. 82.898 and 85.103

e. 83.398 and 84.603

Answer 1

Solution :

Given that,

Sample mean = $\bar x$ = 84

Population standard deviation =   $\sigma$ = 4.5

Sample size = n = 64

At 95% confidence level

$\alpha$ = 1 - 95%  

$\alpha$ = 1 - 0.95 =0.05

$\alpha$/2 = 0.025

Z_$\alpha$/2 = Z_{0.025 =} 1.96

Margin of error = E = Z_$\alpha$/2 * ( $\sigma$ /$\sqrt$n)

= 1.96 * ( 4.5 /  $\sqrt$64 )

= 1.1025

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

T
- E < $\mu$ <
T
+ E

84 - 1.1025 <  $\mu$ < 84 + 1.1025

82.8975 <  $\mu$ < 85.1025

82.898 <  $\mu$ < 85.103

( 82.898 , 85.103 )

The 95% confidence interval for the population mean $\mu$ is between 82.898 and 85.103

Option (d) is correct.