During the test trial phase of a new cell phone product, “Antenna Boost”, certain residents of Monongalia County West Virginia were asked to make cell phone calls with and without Antenna Boost. 1500 random cell phone users were asked to participate in the test. 750 cell phone users were given the Antenna Boost product, and another 750 cell phone users were asked to make cell phone calls without the product. Of the 750 cellphone users testing Antenna Boost, 565 reported a decrease in average service interruptions per day. Of the 750 cellphone users not testing Antenna Boost, 507 reported a decrease in average service interruptions per day. It is known that over 224 million Americans are cellphone users. Is there significant evidence to conclude that the proportion of Antenna Boost users who experience fewer service interruptions is greater than the proportion of users that do not use the product at the a=0.005 level of significance?
Militza and Carlos believe men have a larger shoe size, on average, than women. They asked a random sample of 5 men and 5 women what their shoe sizes were. The results are summarized below. Assume that men and women’s shoe sizes are normally distributed, with standard deviations of 1.2 and 1.4 respectively. Is there significant evidence to prove that men have a larger shoe size than women? Test their claim at the 5% significant level. Men’s Shoe Sizes