Because of the high cost of hospital stays, anything that can reduce their length and the costs of medication would be appreciated by insurance companies, hospitals, and patients. A physician researcher was searching for ways to reduce costs and decided to investigate the effect of the room the patient stayed in. She gathered data on the length of stay and the amount of pain medication (measured in morphine equivalents). Also recorded was whether the room was sunny or dim. Do these data allow the researcher to conclude that the length of stay and the amount of pain medication is lower in bright rooms than in dim ones? Conduct all tests at the 5% significance level. Use a 95% confidence level for estimates. In 2012, there were 221,963,000 Americans aged 21 years or more.
Scrabble is one of the oldest and most popular board games. It is played all over the world, and there is even an annual world championship competition. The game is played by forming words and placing them on the board to obtain the maximum number of points. It is generally believed that a large vocabulary is the only skill required to be successful. However, there is a strategic element to the game that suggests that mathematical skills are just as necessary. To determine which skills are most in demand, a statistician recruited a random sample of fourth-year university English and mathematics majors and asked them to play the game. A total of 500 games was played by different pairs of English and mathematics majors. The scores in each game were recorded. (The authors would like to thank Scott Bergen for his assistance in writing this exercise.)
a. Can we conclude that mathematics majors win more frequently than do English majors?
b. Do these data allow us to infer that the average score obtained by English majors is greater than that for mathematics majors?
c. Why are the results of Parts (a) and (b) not the same?