Question

This discussion board requires you to show ALL work needed to calculate the two confidence intervals below. Please use the formulas for both questions and display each formula for each question below. You will have to use a z table as well.

A random sample of 235 measurements is selected from a population and the sample mean and sample standard deviation are x bar = 32.5 and s = 30.0.

a) Construct a 99% confidence interval to estimate the mean of the population

Answer 1

Solution :

Given that,

= 32.5

s = 30.0

n = 235

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* (s /n)

= 2.576 * (30.0 / 235)

= 5.04

Margin of error is 5.04

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

- E < < + E

32.5 - 5.04 < < 32.5 + 5.04

27.46< < 37.54

(27.5 , 37.5)