Many food products contain small quantities of substances thatwould give an undesireable taste or smell if they are present inlarge amounts. An example is the \"off-odors\" caused by sulfurcompounds in wine. Oenologists (wine experts) have determined theodor threshold, the lowest concentration of a compound that thehuman nose can detect. For example, the odor threshold for dimethylsulfide (DMS) is given in the oenology literature as 25 microgramsper liter of wine (µg/l). Untrained noses may be less sensitive,however. Here are the DMS odor thresholds for 10 beginning studentsof oenology.

41 32 24 35 33 26 36 22 30 31

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

(a) Make a stemplot to verify that the distribution is roughlysymmetric with no outliers. (A normal quantile plot confirms thatthere are no systematic departures from normality. Enter numbersfrom smallest to largest, separated by spaces. Enter NONE for stemswith no values.)

2

2

3

3

4

(b) Give a 95% confidence interval for the mean DMS odorthreshold among all beginning oenology students. (Round youranswers to three decimal places.) ,

(c) Are you convinced that the mean odor threshold for beginningstudents is higher than the published threshold, 25 µg/l? Carry outa significance test to justify your answer. (Use α = 0.05. Roundyour value for z to two decimal places and round your P-value tofour decimal places.) z = P-value =

State your conclusion.

Reject the null hypothesis. There is significant evidence thatthe mean odor threshold for beginning students is higher than thepublished threshold.

Reject the null hypothesis. There is not significant evidencethat the mean odor threshold for beginning students is higher thanthe published threshold.

Fail to reject the null hypothesis. There is significantevidence that the mean odor threshold for beginning students ishigher than the published threshold.

Fail to reject the null hypothesis. There is not significantevidence that the mean odor threshold for beginning students ishigher than the published threshold.