1. The Sloan Survey of Online Learning, "Going the Distance: Online Education in the United States, 2011," reported that 68% of college students believe that online education courses are as good as or superior to courses that use traditional, face-to-face instruction. We want to test if there is evidence that the population proportion is different from .68 at α=.05. In a recent survey, we found that 70% of students in a sample of 100 believe that their online education courses are as good as or superior to courses that use traditional, face-to-face instruction.
a. State the null and alternative hypotheses.
b. State the rejection region.
c. Calculate the test statistic and make a conclusion in the context of the situation given.
2. A University of Florida economist conducted a study of Virginia elementary school lunch menus. During the state-mandated testing period, school lunches exceeded an average of 863 calories. The economist claims that after the testing period ends, the average caloric content of Virginia school lunches drops significantly and is at most 863 calories. In a sample of 100 lunches, the sample mean amount of calories was 865. The sample standard deviation for the number of calories was 10. We want to test economist's claim at α=.01.
a. State the null and alternative hypotheses.
c. Calculate the test statistic.
d. Find the p-value, and make a conclusion in the context of the situation given.
3. Fightmaster and Associates Real Estate, Inc., bases charges to a client on the assumption that telephone surveys can be completed with a mean time of 15 minutes or less. If a greater mean survey time is required, a premium rate is charged the client. Suppose that a sample of 35 surveys shows a sample mean of 17 minutes and a sample standard deviation of 4 minutes. Is the premium rate justified? Test at the alpha=.01 level of significance.
a. State the null and alternative hypotheses.
b. Find the rejection region.
c. Calculate the Test Statistic.
d. State your conclusion in the specific context of this exercise.
4. Joan's Nursery specializes in custom-designed landscaping for residential areas. The labor cost associated with a particular landscaping proposal is estimated based on the number of plantings of trees, shrubs, and so on associated with the project. For cost-estimating purposes, management figures 2 hours of labor time for the planting of a medium-size tree. Actual times from a sample of 8 plantings during the past month are as follows (times in hours). Using a .05 level of significance, we want to test if the mean tree-planting time exceeds 2 hours.
1.9
1.7
2.8
2.4
2.6
2.5
2.8
3.2
a. State the null and alternative hypotheses.
b. Find the sample standard deviation.
c. Calculate the Test Statistic.
d. Find the rejection region.
e. State your conclusion in the specific context of this exercise. What is your conclusion, and what recommendations would you consider making to management?
5. A manufacturer claims that a fuel additive it distributes will yield an increase of at least 4 miles to the gallon for a mid-sized car. A consumer group investigates this claim with a random sample of 12 mid-sized cars. The sample results had a mean increase of 3.7926 miles per gallon and a standard deviation of .4 miles per gallon. Assume the mpg increases form a normal distribution. The consumer group will test if the sample data is extreme enough to reject the manufacturer's claim.
a. What is the parameter of interest in the context of this problem?
b. State the null and alternative for the consumer group.
c. What are the possible decisions here?
d. Clearly describe the Type I and Type II errors for this test in the context of this problem.