Sulfur compounds cause off-odors in wine. Wine experts, oenologists, 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. Untrained noses may be less sensitive, however. You suspect that the mean odor threshold for beginning students is higher than the published threshold =25. Here are the DMS odor thresholds for 10 beginning students of oenology: 31 31 43 36 23 34 32 30 20 24 Assume that the population is normal and the standard deviation of the odor threshold for untrained noses is known to be =7. Find and interpret the 98% confidence interval for the mean odor threshold for beginning students of oenology.

One of your peers claims that boys do better in math classes than girls. Together you run two independent simple random samples and calculate the given summary statistics of the boys and the girls for comparable math classes. In Calculus, 15 boys had a mean percentage of 82.3 with standard deviation of 5.6 while 12 girls had a mean percentage of 81.2 with standard deviation of 6.7. What assumptions need to be made in order to determine the 90% confidence interval for the difference in the mean percentage scores for the boys in calculus and the girls in calculus? Supposing the assumption is true, calculate the interval.