Question

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. The DMS odor thresholds for 10 untrained students are given. 30 30 42 35 22 33 31 29 19 23 (a) Assume that the standard deviation of the odor threshold for untrained noses is known to be ?=7?g/L . To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! Do the three simple conditions hold in this case? Make a stemplot and use it to check the shape of the distribution. Choose the answer that best describes the stemplot. No. Although this is a SRS and ? is known, a stemplot shows that the distribution has many outliers and therefore cannot be Normal. No. Although this is a SRS and ? is known, a stemplot shows that the distribution is not symmetric and therefore cannot be Normal. No, we cannot be sure. Although the stemplot 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 stemplot shows that the distribution is roughly symmetric with no outliers, and ? is known. (b) STATE: What is the average (mean) DMS odor threshold, ? , for all untrained people? PLAN: Using the four‑step process, give a 95% confidence interval for the mean DMS odor threshold among all students. SOLVE: We have assumed that we have a random sample and that the population from which we are sampling is Normal. Find ?¯ . (Enter your answer rounded to one decimal place.) ?¯= ?g/? Find the standard deviation, ??√, of the sampling distribution of ?¯. (Enter your answer rounded to four decimal places.) ??√= CONCLUDE: Choose the correct conclusion. With 95% confidence, the mean sensitivity for all untrained people is between 28.07 to 32.74 ?g/L . With 95% confidence, the mean sensitivity for all untrained people is between 27.56 to 33.24 ?g/L . With 95% confidence, the mean sensitivity for all untrained people is between 26.76 to 33.04 ?g/L . With 95% confidence, the mean sensitivity for all untrained people is between 25.06 to 33.74 ?g/L .

Answer 1

a)Yes, since this is an SRS, a stemplot shows that the distribution is roughly symmetric with no outliers, and ? is known

b)

?¯=29.4

??√, of the sampling distribution of ? =2.2136

With 95% confidence, the mean sensitivity for all untrained people is between 25.06 to 33.74 ?g/L