Question

(18.42) Sulfur compounds cause "off-odors" in wine, so winemakers want to know the odor threshold, the lowest concentration of a compound that the human nose can detect. The odor threshold for dimethyl sulfide (DMS) in trained wine tasters is about 25 micrograms per liter of wine (μμg/ l). The untrained noses of consumers may be less sensitive, however.

You want to estimate the mean DMS odor threshold among all students, and you would be satisfied to estimate the mean to within ±0.1 with 95 % confidence.

The standard deviation of the odor threshold for untrained noses is known to be σ = 9 micrograms per liter of wine.

How large an SRS of untrained students do you need?

Answer 1

Solution :

Given that,

standard deviation = = 9

margin of error = E = 0.1

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 9) / 0.1)²

= 31116.96 = 31117

Sample size = 31117