1. An Asian roulette wheel has 38 numbers; 18 red, 18 black and 2 green. With a perfectly balanced roulette wheel, red numbers should turn up 18 times in 38 spins of the wheel. To test the integrity of the wheel, Luxor Casino records the results of 3,801 plays. Of the 3,801 plays, a red number appeared 1,888 times. Luxor Casino suspects that the roulette wheel favors red numbers more often. (A). State the parameter and statistics in this study. (B). Formulate the null and alternative hypothesis. (C). Compute the test-statistics and p-value. (D). What is your decision and what do you conclude? (use a = 0.10) (E). Construct a 90% confidence interval for the true proportion of red numbers that should appear. 2. Over the past 5 years Zizzo's Caf has infiltrated almost every city in the United States. It has become the \"McDonalds\" of the new millennium. A national survey conducted in 2007 found that Americans consumed on average 97 ounces of coffee per week. An increase in caffeine intake increases the risk for numerous heart related complications and insurance companies want to know if their clients are more at risk to heart complications due to a raise in the national average of coffee consumed. The insurance company surveys 30 adult American citizens and find the average ounces of coffee consumed to be 102.7 ounces with standard deviation of 12.5 (A). State the population and parameter (B). Formulate the null and alternative hypothesis. (C). Compute the test-statistics and p-value. (D). What is your decision and what do you conclude? (use a = 0.10) (E). Construct a 99% confidence interval for the population average ounces of coffee consumed by Americans. 3. Light bulbs of a certain type have a mean lifetime of 850 hours with a standard deviation of 50 hours. Engineers have modified a manufacturing process and believe that their newly designed bulbs should have greater mean life with no change in variability. They plan to put 100 bulbs on life test and reject the null hypothesis in ... of the alternative hypothesis if their average lifetime exceeds 861.63 (A). What is the probability of rejecting the null hypothesis if the mean lifetime is more than 850 hours? (B). What is the probability of retaining the null hypothesis if the mean lifetime is more than 850 hours