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HW #28 – Cautions about CI and HT
1. (IN CLASS) There are signs on the canal banks in Grand Junction telling people to stay off. A questionnaire was sent to Grand Junction residents asking if people still used the canal banks for recreation. Of course, not all questionnaires were returned. A 95% CI is found for the percentage of all Grand Junction residents that use the canal banks for recreation. Will the margin of error (the +/- part) take the non-response into account? Explain.
2. (SOLUTION GIVEN) Have you ever used marijuana? This question is asked to a random sample of people. A 95% CI is found for the percentage of all people that have used marijuana. Do you think we can be 95% sure that the true percentage is in this interval? Explain.
3. (HOMEWORK) On October 2, 2007, on a poll question was asking if the Colorado Rockies Matt Holliday should be the MVP (Most Valuable Player). Do you think a 95% CI for the percentage of all baseball fans that would choose Holliday would have a 95% chance of having the true answer? Explain.
4. (ALTERNATE HW) A sample of 100 people are asked what their favorite fast-food restaurant is. The 100 people were all people having lunch at McDonalds. From the data a 95% CI is obtained to estimate the percentage of all people that would say McDonalds is their favorite fast food restaurant. Do you think there is a 95% chance that the true answer is in this interval? Explain.
5. (IN CLASS) We want to see if we have good evidence that the average time spent per week studying for STAT 200 is more than 5 hours. A SRS of 105 students are surveyed, all students give reasonable answers except one student says they study 1000 hours per week. Suppose a hypothesis is done with all the data and the p-value is .0056. Explain what this means.
6. (SOLUTION GIVEN) We want to see if there is good evidence that more than half of Grand Junction residents use the canal banks for recreation. Questionnaires are sent out, but most are not returned. From the questionnaires that are returned a hypothesis is done and the p-value is found to be .000005551. Explain what this means.
7. (HOMEWORK) We want to see if there is good evidence that the average high temperature in Grand Junction is decreasing. We take as a sample the first 30 days of the year (January 1 through January 30). A hypothesis is done comparing the sample data with the average high temperature for all days throughout the year and the p-value is 0.000000004167. Explain what this means.
8. (ALTERNATE HW) We want to see if there is good evidence that more than half of Americans believe in global warming. A SRS of 100 Americans are taken and are shown Al Gore’s movie “An Inconvenient Truth”, and then asked, “Do you think that global warming is happening?” From the results a hypothesis is done and the p-value is found to be 0.0000009983. Explain what that means.
9. (IN CLASS) Suppose we have data on 60 different physical traits for a SRS of 120 mass murderers and 124 normal people. Suppose we do 60 different hypothesis tests to see if there is any difference between mass murderers and normal people on any of these 60 traits. One test is done for each trait. Suppose for each test we use the 5% significance level for each test.
A) What is the chance that one particular test will mistakenly conclude there is a difference?
B) What is the chance that at least one of the 60 tests will mistakenly conclude a difference by mistake?
10. (SOLUTION GIVEN) Suppose there is a class of 40 STAT 200 students and each is given a test for ESP (physic powers). We will use 5 cards with a square, circle, star, wavy lines, or a triangle. Each student is tested at the 5% level of significance.
A) What is the chance that one particular student will incorrectly be labeled as physic?
B) What is the chance that at least one of the 40 students will mistakenly be labeled as physic?
11. (HOMEWORK) A biologist has data on the density of 55 different plants in a study area from both 1975 and 2005. Hypothesis tests are done for each plant to see if its density has changed over the 30 years. One test for each plant is done. Suppose the 5% level of significance is used for each test.
A) What is the chance that one particular plant will incorrectly be labeled as having changed its density?
B) What is the chance that at least one of the 55 plants will mistakenly be labeled as having changed its density?
12. (ALTERNATE HW) A biologist traps mice in two different areas and checks the mice for 15 different diseases. Hypothesis tests are done for each disease to see if there is any difference in the preponderance of the diseases between the two areas. One test for each disease is done. Suppose the 5% level of significance is used for each test.
A) What is the chance that one particular disease will incorrectly be labeled as being different in the two areas?
B) What is the chance that at least one of the 15 diseases will incorrectly be labeled as being different in the two areas?
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