Question

3. Small amounts of sulfur compounds are often present in wine. Because these compounds have unpleasant odors, wine experts have determined the odor threshold, the lowest concentration of a compound that a trained human nose can detect. For example, the odor threshold for dimethyl sulfide (DMS) is 25 micrograms per liter of wine (µg/l). Untrained noses may be less sensitive, however. A wine researcher found the DMS odor thresholds for 10 students in his restaurant management class. Here are the data. 31 31 43 36 23 34 32 30 20 24 Assume that the standard deviation of the odor threshold for untrained noses is known to be σ = 7 µg/l.

a. Is it reasonable to assume the data are from an approximately normal population? Explain.

b. The researcher believes that the mean odor threshold for beginning students is higher than the published threshold, 25 µg/l, and decides to conduct a significance test. What are the null and alternative hypotheses?

c. Carry out a significance test. Report the value of the test statistic, the p-value, and your conclusion.

Answer 1

Yes, it is reasonable to assume the data are from an approximately normal population. Because of known population standard deviation. (6) Null hypothesis: H:= 25 The mean odor threshold for beginning students is 25 ugl. Alternative hypothesis: H4> 25 The mean odor threshold for beginning students is higher than the published threshold. 25 ugl.

EXCEL (PH Stat) output: Z Test of Hypothesis for the Mean 25 Data Null Hypothesis u= Level of Significance Population Standard Deviation Sample Size Sample Mean 0.05 7 10 30.4 Intermediate Calculations Standard Error of the Mean Z Test Statistic 2.2136 2.4395 Upper-Tail Test Upper Critical Value p-Value Reject the null hypothesis 1.6449 0.0074 Test Statistic: z = 2.44. p-value = 0.0074. Conclusion:

Use a significance level, a = 0.05. Here, p-value is 0.0074, which is less than the value of a -0.05. That is, p-value (=0.0074) a(=0.05). Therefore, by the rejection rule, reject the null hypothesis H. Interpretation: There is sufficient evidence at level of significance a = a = 0.05. The mean odor threshold for beginning students is higher than the published threshold, 25 ugl.