Question

Suppose x has a mound-shaped distribution. A random sample of size 16 has sample mean 10 and sample standard deviation 2.

(b) Find a 90% confidence interval for μ

(c) Interpretation Explain the meaning of the confidence interval you computed.

Answer 1

Solution :

Given that,

(a)

Point estimate = sample mean = = 10

sample standard deviation = s = 2

sample size = n = 16

Degrees of freedom = df = n - 1 = 15

t _/2,df = 1.753

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

= 1.753 * (2 / 16)

Margin of error = E = 0.9

The 90% confidence interval estimate of the population mean is,

- E < < + E

10 - 0.9 < < 10 + 0.9

9.1 < < 10.9

(9.1 , 10.9)

(b)

The 90% confidence interval estimate of the population mean is, 9.1 to 10.9