Question

Suppose you have a sample of data, where x? = 20, s = 4, n = 36. Suppose you want to create a confidence interval for the mean, where alpha (?) = .01

What is the best point estimate, critical value, margin of error, lower bound, and upper bound used for the confidence interval?

Answer 1

Solution :

Given that,

Point etimate = = 20

s = 4

n = 36

Degrees of freedom = df = n - 1 = 36 - 1 = 35

= 0.01

/ 2 = 0.01 / 2 = 0.005

Critical value = t _/2,df = t_0.005,35 = 2.724

Margin of error = E = t_/2,df * (s /n)

= 2.724 * (4 / 36)

= 1.8

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

- E < < + E

20 - 1.8 < < 20 + 1.8

18.2 < < 21.8

(18.2 , 21.8)

Lower bound = 18.2

Upper bound = 21.8