solution

 

. Many food products contain small quantities of substances that would give an undesirable taste or smell if they were present in large amounts. An example is the “off-odors” caused by sulfur compounds in wine. Oenologists (wine experts) have determined the odor threshold, the lowest concentration of a compound that the human nose can detect. For example, the odor threshold for dimethyl sulfide (DMS) is given in the oenology literature as 25 micrograms per liter of wine (μg/l). Untrained noses may be less sensitive, however. Here are the DMS odor thresholds for 10 beginning students of oenology:

$1rn 31$1rn 31    43$1rn 36$1rn 23    34$1rn 32$1rn   30$1rn  20$1rn  24

Assume (this is not realistic) that the standard deviation of the odor threshold for untrained noses is known to be σ = 7 μg/l.

(a) Make a stemplot to verify that the distribution is roughly symmetric with no outliers. (A Normal quantile plot confirms

that there are no systematic departures from Normality.)

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

(c) Are you convinced that the mean odor threshold for beginning students is higher than the published threshold, 25 μg/l?

Carry out a significance test to justify your answer.