Question

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 (μg/l). The untrained noses
of consumers may be less sensitive, however. Here are the DMS odor thresholds for 10 untrained students:

31 31 43 36 23 34 32 30 20 24

(a) Assume that the standard deviation of the odor threshold for untrained noses is known to be σ = 7 μg/l. Briefly discuss the other two “simple conditions,”
using a stemplot to verify that the distribution is roughly symmetric with no outliers.

(b) Give a 95% confidence interval for the mean DMS odor threshold among all students.

Answer 1

a)

stem leaf plot

stem	leaf
2	0 3 4
3	0 1 1 2 4 6
4	3

from plot, data is symmetrically distributed

b)

Level of Significance ,    α =    0.05          
'   '   '          
z value=   z α/2=   1.96   [Excel formula =NORMSINV(α/2) ]      
                  
Standard Error , SE = σ/√n =   7.0000   / √   10   =   2.2136
margin of error, E=Z*SE =   1.9600   *   2.2136   =   4.3386
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    30.40   -   4.338565   =   26.0614
Interval Upper Limit = x̅ + E =    30.40   -   4.338565   =   34.7386
95%   confidence interval is (   26.061   < µ <   34.739   )