1. The manager of an accounting office is studying the problem of incorrect account numbers being entered into the computer system and wishes to produce a p chart. A subgroup of 200 account numbers is selected from each day's entries and checked to determine the number of incorrect entries. The average proportion of such incorrect entries for the last several months is 0.12.

2. The National Centre for Health Statistics reports that the mean systolic blood pressure for males 35-44 years of age is 128 and a standard deviation of 15. A group of 50 executives selected at random are tested and found to have an average of 132.3. Is there statistical evidence that the executives have a different blood pressure than the population? Use a significance level of 0.05. Solve using a confidence interval approach or a hypothesis test.

3. A local donut shop wishes to test out its donuts against those of the competition which is planning to set up in the community. Each of 50 subjects tastes two unidentified donuts and says which is preferred. Thirty-one or 62% of the subjects prefer the local company donuts to the competition's donuts. Test the claim that a majority (over 50%) of people prefer the local company donuts at the significance level of 0.01.