1. Suppose a certain fast food chain claims that customers only wait an average of 2.4 minutes on drive through orders. Believing that the food chain has made a false claim, a certain analyst takes a random sample of 45 drive-thru orders and determines that the 45 customers wait an average of 2.7 minutes with a standard deviation of 0.6 minutes. Is there sufficient evidence to conclude that the true average waiting time for drive-thru orders at this particular fast food chain is actually more than the claimed 2.4 minutes? Be sure to identify all parts of the test, and write your conclusion in the context of this scenario.
2. Suppose a large labor union wants to estimate the mean number of hours each month that its members are absent from work. The union randomly samples 320 of its members and records the mean number of hours each of them is absent from work in a one-month period. If the average is found to be 8.2 hours with a standard deviation of 5.5 hours, estimate the true mean number of hours all union members are absent from work per month with 90% confidence.
3. In a 2006 poll of a random sample of 2546 American 18 – 24 year olds taken by Harvard’s Institute of Politics, 16% reported that they regularly watch The Daily Show with John Stewart. Estimate the true proportion of college age students who regularly watch this show with 90% confidence.
4. The US Commission on Crime wants to estimate the proportion of crimes related to firearms in an area that has one of the highest crime rates in the country. The commission randomly selects 500 files of recently committed crimes in the area and finds that 320 involved the use of a firearm.
a. Estimate the percentage of all crimes in this area in which a firearm was used with 95% confidence.
b. Would the confidence interval become wider or narrower if we lowered the level of confidence?
c. Explain what 95% confidence means in the context of this problem.
5. A method currently used by doctors to screen for a particular type of cancer fails to detect cancer in 10% of the patients who actually have the disease. A new screening method has been developed, and doctors hope that the failure rate of this test will be smaller. A random sample of 75 people who are known to have this type of cancer is screened using the new technique, and the new method fails to detect the cancer in 6 of the patients. At the 0.05 level, test the appropriate hypothesis to determine if the new method has lowered the failure rate.
6. Suppose a management professor wants to estimate with 99% confidence the proportion of CEO’s of medium and large companies with no university degrees.
a. How large should the professor’s sample be to ensure an estimate that is within 0.05 of the true proportion?
b. How large should the professor’s sample be to ensure an estimate that is within 0.02 of the true proportion?
c. If a previous study indicates that about 10% of CEO’s of medium and large companies have no university degrees, how many CEO’s should be sampled by the professor to maintain a margin of error that is no more than 0.02?