1) A random sample of 49 drinks from a beverage dispensing machine gave an average of 12.2 ounces with a standard deviation of 0.7 ounces. At a 2% level of significance can you conclude that the true mean beverage dispensed by the machine is more than 12 ounces?

2) The costs associated with conducting interviews for a job opening have skyrocketed over the years. According to a Harris interactive survey, 211 of 502 senior human resources executives at U.S. companies believe that their hiring managers are interviewing too many people to find qualified candidates for the job. Construct a 98% confidence interval for the true proportion of human resource executives who believe that their hiring managers are interviewing too many people.

3) An aspirin manufacturer fills bottles by weight rather than by count. Since each bottle should contain 100 tablets, the average weight per tablet should be 5 grains. Each of 100 tablets taken from a very large lot is weighed resulting in a sample average weight per tablet of 4.87 grains and a sample standard deviation of 0.5 grain. At a 1% level of significance does this provide a strong evidence to conclude that the company is not filling its bottles as advertised? Use the rejection region method to do this problem (and not the p-value method).