Question

We study the average size of a new hybrid plant. We have a small random sample in size n = 5 plants. Here are five height in meters:

0.85, 1.07, 0.79, 0.93 and 0.82.

Consider this example as a preliminary study. What is the sample size required so that the error in estimation of the average does not exceed 0.025 meters at a confidence level of 95%?

Answer 1

We calculate the mean and sd from the given sample by making use of the following table:

	size	x^2
	0.85	0.7225
	1.07	1.1449
	0.79	0.6241
	0.93	0.8649
	0.82	0.6724
Total	4.46	4.0288

Variance

  

We know that the margin of error is critical value*SE

The critical value for a 95% confidence is 1.96.

The standard error is

Given that the margin of error does not exceed 0.025

ie

  

The sample size should be n=77 for the margin of error should not exceed 0.025