Review Questions for Statistical Inference
(chapter 10) An economist says that a 90 percent confidence interval for the response of driving to a $1 increase in the price of gasoline is a decline of 4 percent in miles driven, plus or minus 0.8 percent. This is based on a survey of the driving behavior of 300 people. Explain what the confidence interval means.
(chapter 10) Define the following terms: significance level; power; statistically significant; type I error; type II error; two-sided alternative hypothesis
(chapters 11, 12, and 13). For the following problems, state the type of test (t-test, two-sample t-test, matched-pairs t-test, one-prop z-test, two-prop z-test, chi-square goodness-of-fit test, chi-square independence test)
- In 1990, when asked if they were optimistic about the future, 20 percent of people said they strongly agreed, 40 percent said that they mostly agreed, 30 percent said they mostly disagreed, and 10 percent said they strongly disagreed. In 2000, the percentages were 15, 32, 51, and 2, respectively. Was there a significant difference in the responses in 2000?
- In 1990, 24 out of 200 of people said that they were worried about global warming. In 2000, 27 out of 181 people said they were worried about global warming. Were the results significantly different?
- The null hypothesis is that free-range chickens weigh 5.0 pounds. The alternative hypothesis is that they weight less. We take a sample of 12 free-range chickens, and the average weight is 4.7 pounds with a standard deviation of .5 pounds.
- At a restaurant, out of 100 women, 30 order chicken, 10 order steak, and 60 order vegetarian. Of 100 men, 25 order chicken, 23 order steak, and 42 order vegetarian. Are the differences for the eating choices of men and women statistically significant?
- Two varieties of wheat are planted in each of five farms. The five farms are in various parts of the country, with large differences in soil quality, rainfall, and other factors. On the first farm, variety A yields 3.1 bushels per acre and variety B yields 2.8 bushels per acre. For farm two, the yields are 4.6 and 4.5. For farm three, the yields are 2.2 and 2.9. For farm four, the yields are 8.1 and 7.1. For farm five, the yields are 3.3 and 3.2. Is there a significant difference in the yields of the two varieties?