What is the z value? What is the P value? Sulfur compounds cause \"off-odors\" i

Question

What is the z value? What is the P value?

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 27 micrograms per liter of wine (µg/l). The untrained noses of consumers may be less sensitive, however. Here are the DMS odor thresholds for 10 untrained students. 36 32 32 28 34 31 27 29 28 29 Assume that the odor threshold for untrained noses is Normally distributed with = 6 µg/l. Is there evidence that the mean threshold for untrained tasters is greater than 27 µg/l? (Use = 0.05.)

Explanation / Answer

here std error = /(n)1/2 =1.897

hence test stat =(X-mean)/std error=(30.6-27)/1.897=1.898

for above test stat p value =0.029

as p value is less then 0.05 level; we reject null hypothesis, and conclude that there is  evidence that the mean threshold for untrained tasters is greater than 27 µg/l

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