You want to estimate the mean DMS odor threshold among all students, and you wou

Question

You want to estimate the mean DMS odor threshold among all students, and you would be satisfied to estimate the mean to within ±0.25 with 95% confidence.

The standard deviation of the odor threshold for untrained noses is known to be = 7 micrograms per liter of wine.

How large an SRS of untrained students do you need?

(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 ( g/ 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 ±0.25 with 95% confidence.

The standard deviation of the odor threshold for untrained noses is known to be = 7 micrograms per liter of wine.

How large an SRS of untrained students do you need?

Explanation / Answer

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.025  
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
s = sample standard deviation =    7  
E = margin of error =    0.25  
      
Thus,      
      
n =    3011.703715  
      
Rounding up,      
      
n =    3012   [ANSWER]

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