Statistical Methods

3.6.1.1.Examples

Unit 3 - Estimation

3.6.1.1.Examples
Example1
From a random sample of 25 fishes taken from a pond, the average length is found to be 5.2cm.Assuming the length follows a normal distribution with an unknown mean and a standard deviation of 0.5 cm.
1.Calculate the 95% Confidence Interval for the mean length of fishes in the pond.

For a confidence level of 95%, the critical value is z_α/2 = 1.96.

2.Indicate the sample size needed to estimate the average length with an error of ± 0.5 cm and a confidence level of 95%.


Example 2
A sample of the sixteen fishes has been taken from a pond gave the following length measurements in mm.
95, 108, 97, 112, 99, 106, 105, 100, 99, 98, 104, 110, 107, 111, 103, 110.
Assuming that the length fishes follow a normal distribution with variance of 25 mm2 unknown mean:
1. What is the distribution of the sample mean?

2. Determine the confidence interval at 95% for the population mean.

Example 3
With a confidence level of 90%, what would the minimum sample size need to be in order for the true mean of the length to be less than 2 cm from the sample mean?