Question

Construct a 99% confidence interval to estimate the population mean using the data below. x = 380=10 n=49 With 99% confidence, when n = 49 the population mean is between a lower limit of (Round to two decimal places as needed.) and an upper limit of . Enter your answer in the edit fields and then click Check Answer. All parts showing Clear All

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 38

Population standard deviation =   $\sigma$ = 10

Sample size = n =49

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 * ( 10/ $\sqrt$ 49)

= 3.68

At 99% confidence interval is,

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

38-3.68 < $\mu$ <38+3.68

34.32< $\mu$ < 41.68

(34.32,41.68)

lower limit 34.32.

upper limit 41.68