Question

A random sample of size 16 from a normal distribution with known population standard deviation � = 3.1 yields sample average � = 23.2.

What probability distribution should we use for our sampling distributions of the means?

a) Normal Distribution

b) T-distribution

c) Binomial Distribution

d) Poisson Distribution

What is the error bound (error) for this sample average for a 90% confidence interval?

What is the 90% confidence interval for the population mean?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 23.2

Population standard deviation = = 3.1

Sample size = n = 16

a) Normal Distribution

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (3.1 / 16)

= 1.27

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

- E < < + E

23.2 - 1.27 < < 23.2 + 1.27

21.9 < < 24.5

( 21.9 , 24.5 )