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 8.34 mm and a standard deviation of 1.417 mm. Use these measurements as a pilot study to determine the sample size needed to estimate the true average diameter to within 0.30 mm with 90% confidence. Your answer should be a whole number.

Answer 1

Given :  $\sigma$ = 1.417 mm,  $\alpha$ = 0.10 & Margin of error = E = 0.30 mm

To find : n = ?

Solution : In general,
E =  $Z_{\alpha/2}*\sigma*\frac{1}{\sqrt{n}}$
where Z ($\alpha$/2) = Z (0.05) = 1.6449

Thus,
0.30 =
1.6449 * 1.417 * n

i.e. n = 60.3637  $\approx$60.

Hope this answers your query!