Warm Up According to a 2014 study from the University of Michigan, 24.5% of 16-year-olds in the U.S. have their driver’s license. You believe the percentage in San Jose is even lower, so you take a random sample of 90 16-year-olds in San Jose and find that only 17 of them have their driver’s license. Is this convincing evidence that a lower percentage of San Jose 16-year-olds have their driver’s license than 16-year-olds in the U.S.? You may assume the conditions for inference are met in this case.

Warm Up – Follow-up In the warm-up problem Ho was p = 0.245 and Ha was p < 0.245. The value of p-hat was 0.189 and the p-value was 0.108. Which of the following best describes what the p-value measures? a) 0.108 is the probability of obtaining a p-hat value of 0.189 or lower from a sample if the true proportion is 0.245. b) 0.108 is the probability of obtaining a p-hat value of 0.189 or higher from a sample if the true proportion is 0.245. c) The probability that the true proportion of 16-year-olds in San Jose with a driver’s license is lower than 0.245 is 0.108. d) The probability that the true proportion of 16-year-olds in San Jose with a driver’s license is equal to 0.245 is 0.108.

t Test Practice #1 Data was collected on the actual speed of a car when its speedometer read 50 mph. All of the cars tested were the same model. For the 12 cars tested the mean speed measured was 52.7 mph and the standard deviation was 4.8 mph. Construct a significance test to determine if the mean speed of the cars is above 50 mph using a = 0.05. (assume all conditions for inference are satisfied)

t Test Practice #2 A national study published in 2006 found that, during an 8 hour day, the average office worker spent 2 hours “goofing off” (using social media, emailing friends, etc.). A local business manager wants to determine if his employees are different from the rest of the nation. He randomly selected 10 employees and secretly installed a video camera in their office cubicles. The video was reviewed and the number of minutes spent “goofing off” by each employee was found to be: 112 117 130 111 131 113 113 105 128 Is there significant evidence this company’s employees are different from the rest of the nation? (use a = 0.05)

Paired t Test Practice A 2004 study investigated the use of chocolate milk as a recovery aid. Nine cyclists drank either chocolate milk or a carbohydrate replacement drink after exercising. Then each cyclist performed an endurance routine until exhausted. The experiment was then repeated for the other drink. The exercise time until exhaustion is given below. Is this statistically significant evidence that the mean time to exhaustion is longer with chocolate milk? (a = 0.01) Cyclist 1 2 3 4 5 6 7 8 9 C. Milk 24.8 50.1 38.3 26.1 36.5 26.1 36.1 47.3 35.1 Carbo 10.0 29.9 37.4 15.5 9.1 21.6 31.2 22.0 17.0