Question

Salal (Gaultheria shallon) is a shrub native to western North America. The young leaves and the dark blue berries of the shrub are edible, and both have been long used by indigenous people in western Canada. The berries in particular are commonly used as a sweetener in cooking. In a particular region of Vancouver Island, 10 dark blue salal berries were randomly sampled and their diameters were measured, giving a mean of 8.12 mm and a standard deviation of 1.209 mm. Use these measurements as a pilot study to determine the sample size needed to estimate the true average diameter to within 0.20 mm with 95% confidence. Your answer should be a whole number. Answer:

Answer 1

Given data,
margin of error =0.20
standard deviation is 1.209
confidence level is 95%
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Zα/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 1.209
ME =0.2
n = ( 1.96*1.209/0.2) ^2
= (2.37/0.2 ) ^2
= 140.38 ~ 141          
sample size = 141