Some chemists wanted to test the effectiveness of a new fertilizer. They used 12 plots of land from around the country. Each plot was divided into two equal sub-plots, one of which was treated with the currently used fertilizer and the other of which was treated with the new fertilizer. Wheat was planted on all of the sub-plots, and the yield was measured. Are the following yields (listed at the bottom of the page) different at the .05 significance level?

The publisher of the Yellow Pages took a sample of 40 retail stores that did not advertise in the Yellow pages in one of the last two years, but did advertise in the other year. The difference in annual sales, in thousands of dollars, between the year advertised and the year not advertised was 19.75. The standard deviation of the differences was 30.24 and the "s" statistic was 30.63. Are the sales totals different at the .90 confidence level?

The HR department of a company is deciding whether to sponsor a lunchtime exercise program to improve workers' health and therefore lessen health insurance premiums paid by the company. They ran a sample program in one plant, recording medical expenses for each participant during the twelve months prior to the program and during the twelve months after the program. Are these expenses, expressed in thousands of dollars and listed at the bottom of the page for each month of the year, different at the 95% confidence level?

A pharmaceutical company is testing the effectiveness of a new sleeping pill. They measure the length of time it takes various volunteers to fall asleep after either taking the sleeping pill or taking a similar pill with no drugs in it. Each of 50 volunteers takes one of the pills at random each week. The average time taken to fall asleep is 21.05 minutes with the "real" pill and 24.52 minutes with the "placebo" pill. Therefore, the difference in time taken to fall asleep after taking the pill is –3.47, the standard deviation of the differences is 9.94, and the "s" statistic is 10.04 minutes. Are these times different at the .05 significance level?