Question

Score: 0 of 1 pt For the provided sample mean, sample size, and population standard deviation, complete parts (a) through (c) below. x#21,n-100, σ 2 Find a 95% confidence interval for the population mean. The 95% confidence interval is from | | to (Round to two decimal places as needed.) Enter your answer in the edit fields and then click Check Answer. parts remaining

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 21

Population standard deviation = $\sigma$ = 2

Sample size = n = 100

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z_$\alpha$/2 = Z_0.025 = 1.96

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

= 1.96 * ( 2 / $\sqrt$ 100)

= 0.39

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

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

21 - 0.39 < $\mu$ < 21 + 0.39

20.61 < $\mu$ < 21.39

The 95% confidence interval is from (20.61 to 21.39)