Question

The basal area of a tree is a conceptual measure. The diameter of a tree is measured at breast height (4.5 feet above ground) and assumed to be the diameter of a circle. The area of this circle is the basal area (BA) of the tree. Assuming that the diameters have a standard deviation of 2 inches and are normal distributed (which typically they do not), how many samples are required to keep the sample mean diameter within 1 inch of the population mean diameter 90% of the times?

Answer 1

Solution :

Given that,

Population standard deviation = = 2

Margin of error = E = 1

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

sample size = n = (Z_/2* / E) ²

n = (1.645 * 2/ 1)²

n = 10.82

n = 11

Sample size = 11

11 samples are required to keep the sample mean diameter within 1 inch of the population mean diameter 90% of the times.