Question

Suppose that X has distribution N(μ, 4). A sample of size 25 yields a sample mean X = 78.3. Obtain a 99-percent (two-sided) confidence interval for μ.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 78.3

Variance = ² = 4

Population standard deviation = = 2

Sample size = n = 25

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( /n)

= 2.576 * (2 / 25 )

= 1.03

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

- E < < + E

78.3 - 1.03 < < 78.3 + 1.03

77.27 < < 79.33