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. here are the dms odor thresholds for 10 untrained students:

30 30 42 35 22 33 31 29 19 23

data set

assume that the standard deviation of the odor threshold for untrained noses is known to be ? = 7 ? g/l.

step 1:
do the three simple conditions hold in this case? use a boxplot to check the shape of the distribution.

no. although this is a srs and ? is known, a boxplot shows that the distribution is not symmetric and therefore cannot be normal.

no. although this is a srs and ? is known, a boxplot shows that the distribution has many outliers and therefore cannot be normal.

no, we can? t be sure. although the boxplot looks roughly normal and ? is known, these 10 students are not an srs of the population in general, and without any more information on how they were chosen, they may not even be an srs of the student population.

yes, since this is an srs, a boxplot shows that the distribution is roughly symmetric with no outliers, and ? is known.

step 2:
following the four-step process, give a 95% confidence interval for the mean dms odor threshold among all students.

27.56 to 33.24
28.07 to 32.74
26.76 to 34.04
25.06 to 33.74