Assignment 16: Testing Claims on Proportions 1. Which of the following can be thought of as representing areas? p-value z-value critical value a test statistic critical region 2. If we fail to reject the null, does that mean the null is true (Yes/No)? 3. In previous years in a metro region, typically 6 out of any 30 days have had excessively long commute times. People suspect this may have since decreased due to recent improvements in the public transport system. Data from a simple random sample of 30 days from the past year show that only 3 days had the long commutes. We will test to see if the proportion of days with long commutes is now less than it was before the transit improvements. Test the claim using a = .02. When you have found the test statistic, use a calculator to approximate it, rounded to 2 decimal places. (a) Use the p-value method. (b) Use the critical value method, including a picture shading the critical region(s) and showing the test statistic. (c) True/False: The evidence does not support the claim that the proportion of long commutes has decreased. (d) True/False: We can conclude that the proportion of long commutes is truly 6/30. 4. As you did on the homework, consider a ight to be on time if it arrives no later than 15 minutes after the scheduled arrival time. Of 48 American Airlines ights from New York (JFK) to Los Angeles (LAX) during a recent January, 44 of them were on time. Use this sample to test the claim made by CNN recently that 79.5% of ights are on time, using a .01 signicance level