Sulfur compounds cause “off-odors” in wine, so winemakers want to

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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 (µg/l). The untrained noses of consumers may be less sensitive, however. Here are the DMS odor thresholds for 10 untrained students: 31 31 43 36 23 34 32 30 20 24

Assume that the odor threshold for untrained noses is Normally distributed with a population standard deviation of 6.7mg/l.

1. At a 0.05 significance level, test the claim that the mean threshold for untrained tasters is greater than 25µg/l.

   i. State the null and alternative hypotheses.

  ii. State the significance level for this problem.

  iii. State the test statistic.  

  iv. State the P-value.

   v. State whether you reject or do not reject the null hypothesis.

   vi. State your conclusion in context of the problem.

   vii. If the true mean was 30.8 µg/l, did you make an error?  If so, which error? Why?