Question

Construct a 99​% confidence interval to estimate the population mean using the data below.

x̅ = 44 σ= 8 n=42

With 99​% confidence, when n=42 the population mean is between a lower limit of ___ and an upper limit of ___

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 44

Population standard deviation =   $\sigma$ = 8
Sample size = n =42

At 99% confidence level the z is ,

$\alpha$  = 1 - 99% = 1 - 0.99 = 0.01

$\alpha$ / 2 = 0.01 / 2 = 0.005

Z$\alpha$/2 = Z0.005 = 2.576   ( Using z table )

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

= 2.576 * (8 / $\sqrt$ 42)

= 3

At 99% confidence interval estimate of the population mean is,

$\bar x$- E < $\mu$ < $\bar x$ + E

44 - 3 , 44+3

(41 , 47)

lower limit of _41__ and an upper limit of _47__