Many food products contain small quantities of substances that would give an und

Question

Many food products contain small quantities of substances that would give an undesireable taste or smell if they are present in large amounts. An exaple 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.

Assume (this is not realistic) that the standard deviation of the odor threshold for untrained noses is known to be = 7 µg/l. A normal quantile plot confirms that there are no systematic departures from normality.

(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. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

(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. (Use = 0.05. Round your value for z to two decimal places and round your P-value to four decimal places.)

34 41 26 23 32 31 36 35 30 20

Explanation / Answer

a) Stem and Leaf

c) H0: Mu<= 25

Ha: Mu >25

alpha:5% level

Test statistic:

From data sample mean=30.8

z= 2.6202

P value= 0.004

P <0.05 we reject the H0. Hence claim is significant

Stem Leaf 4 1 3 5 6 3 0 1 2 4 2 6 2 0 3

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