Hypothesis Testing for Studies: Example Problems

As part of a study of corporate employees, the director of human resources for PNC, wants to compare the distance traveled to work by employees at its office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 35 Cincinnati employees showed they travel a mean of 370 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month. The population standard deviation for the Cincinnati and Pittsburg employees are 30 and 26 miles respectively. At the .05 significance level is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburg employees?

The Roper Company conducted identical surveys 5 years apart. One question asked of women was are most men basically kind, gentle and thoughtful? The earlier survey revealed that, of the 3,000 women surveyed, 2,010 said that they were. The later revealed 1,530 of the 3,000 women surveyed thought that men were kind, gentle and thoughtful. At the .05 level, can we conclude that women think men are less kind, gentle, and thoughtful in the later survey compared with the earlier one?

The research department at the home office of New Hampshire Insurance conducts on-going research on the causes of automobile accidents, the characteristics of the drivers, and so on. A random sample of 400 policies written on a single persons revealed 120 had at least one accident in the previous three year period. Similarly, a sample of 600 policies written on married persons revealed that 150 had been in at least one accident. At the .05 significance level, is there a significant difference in the proportions of single and married persons having an accident during a three year period?