Question

Question 3

A confidence interval for the population mean when the population follows the normal distribution and the population standard deviation is known is computed by? Provide examples.

Question 6

What are the factors that determine the sample size? How is sample size calculated for estimating the population mean? Provide examples

Answer 1

Question 3:

A confidence interval for the population mean when the population follows the normal distribution and the population standard deviation is known is computed by using z-interval formula and the formula is

Example 1: We are given that sample mean = 25, confidence level c = 0.95, population sd =5 and sample size n = 36

Using statistical table we get zc = 1.96 for confidence level c = 0.95

Now we plug the values in the formula.

So the 95% confidence interval for population mean is (23.37,26.63)

Example 2: We are given that sample mean = 42, confidence level c = 0.99, population sd = 5 and sample size n = 16

Using statistical table we get zc = 2.58 for confidence level c = 0.99

Now we plug the values in the formula.

So the 99% confidence interval for population mean is (38.775,45.225).

Question 6:

Factors to determine the sample size n for estimating the population mean are , confidence level c,population standard deviation and margin of error E.

Example 1: Determine sample size n, when confidence level c = 0.95, population sd = 15 and margin of error E = 4

Using table zc = 1.96 .Sample size formula is,

Example 2 :

Determine sample size n, when confidence level c = 0.98, population sd = 10 and margin of error E = 6

Using table zc =2.33 and Sample size formula is,