A statistics instructor has written a new placement exam. The department chair would like to use this new exam, but is concerned that it may be too long. Students will be given one hour to complete the exam. The exam will be used if there is sufficient evidence to conclude that the mean time to complete the exam is less than 50 minutes. The new exam is given to a random sample of 36 students and a sample mean time to complete the exam was 48 minutes with a sample standard deviation of 5. State the hypotheses to be tested and perform the test using a significance level of 0.05.

Suppose that the unemployment rate in the U.S. is 0.05 . A random sample of 2000 adult residents residents resulted in 125 respondents who were unemployed. Test the hypothesis that the unemployment rate is greater than 0.05. Alpha = 0.01.

It is assumed that 30% of all M&Ms are dark brown. What is the probability that you would open a package containing 68 M&Ms and more than 30 were dark brown?