Conduct a hypothesis test for each problem, using the traditional method.
1. A random sample of 56 departing flights at an airport over a 3-month period had a mean wait of 14.2 minutes between boarding and takeoff, with a standard deviation of 4.53 minutes. At the same airport, a random sample of 81 incoming flights over the same 3-month period had a mean wait of 17.5 minutes between the time that the plane arrived at the gate and the time that the baggage reached the baggage claim area, with a standard deviation of 9.87 minutes. At the 0.05 level of significance, test the claim that at this airport the mean wait for takeoff is less than the mean wait for baggage.
2. A math instructor has written a new placement exam. He is concerned that the exam may be too long. The instructor claims that the average length of time required to finish the exam for all students who take it is at most 50 minutes. The exam is given to 20 randomly selected students, and their average length of time required to finish the exam was 54 minutes, with a standard deviation of 5.99 minutes. Test the instructor's claim at the 0.05 level of significance.
3. A physician claims that 13.6% of all pregnant females smoke during their pregnancy. A random sample of 400 pregnant women revealed that 60 of them are smoking while pregnant. Test the physician's claim at the 0.05 level of significance.
[[4. A random telephone survey asked 208 drivers if they run red lights. Of the 48 drivers who were 35 years old or younger, 32 admitted that they run red lights. Eighty-six of the 160 drivers that were older than 35 years old admitted to running red lights. At the 0.01 level of significance, test the claim that the percent of drivers who are 35 years old or younger and who run red lights is higher than the percent of drivers who are older than 35 years old and who run red lights.]] * Solution to number 4 is not included in the response.
5. Test the claim that the mean time Americans spend watching TV per day is 4.4 hours at the 0.10 level of significance. A random sample of 80 people had a mean time of 2.225 hours viewing per day and a standard deviation of 1.088 hours.
6. Tests in a professor's past statistics classes have scores with a standard deviation equal to 14.1. One of her current classes now has 27 test scores with a standard deviation of 9.3. Use a 0.01 level of significance to test the claim that the standard deviation of this current class is less than 14.1.
This solution shows step-by-step calculations in hypothesis testing starting with stating the decision rule, calculating the test statistic, comparing it to the p-value and make a final decision to accept or reject the null hypothesis.