Section 8 - 3 : Testing a Claim About the Population Mean 1. Mr. Eitel thinks that the average time spent on homework by all the students in his statistics class is 4.2 hours a week. His students say that he is wrong. They claim that the average time the students spend on homework is more than 4.2 hours a week. They take a random sample of 46 students and find that the average time spent on homework for students in the sample was 4.5 hours with a standard deviation of .72 hours. Test the claim at a .01 significance level that the average time his statistics students spend on homework is more than 4.2 hours a week. Ho Sample Mean: H : Sample Standard Deviation: Graph of Critical information: Test Statistic: Conclusion based on Ho : Conclusion based on the problem: There sufficient evidence at the significance level to the claim that2. After standing in line to buy books at the campus bookstore a student complains that the average wait time is 24 minutes. The bookstore records the wait time for 41 students selected at random. The bookstore finds that the average wait time for these 41 students was 22.5 minutes with a standard deviation of 3.1 minutes. Test the claim at a .05 significance level that the mean wait time for students at the FLC bookstore is less than 24 minutes. Ho Sample Mean: Sample Standard Deviation: Graph of Critical information: Test Statistic: Conclusion based on Ho : Conclusion based on the problem: There sufficient evidence at the _ significance level to the claim that3. A weight watchers advertisement claims that the average weight loss for all it's clients is 4.6 pounds in the first month. A consumer group complained about the advertisement. They claimed that the average loss for a client is not 4.6 pounds in the first month. They took a random sample of 32 weight watcher's clients and found they had an average weight loss of 4.4 pounds with a standard deviation of .99 pounds. Test the claim at a .10 significance level that the average weight loss in the first month is not equal to 4.6 pounds. Ho Sample Mean: H: Sample Standard Deviation: Graph of Critical information: Test Statistic: Conclusion based on Ho : Conclusion based on the problem: There sufficient evidence at the significance level to the claim that4. A college recruiting advertisement boasts that the average class size at their college is 41.5 students per class. A newspaper thinks that the class average was more than 41.5 students per class. To help settle the issue the reporter conducted a random sample of 56 sections held at the college. The sample data showed that the average class size was 42.8 students per class with a standard deviation of 5.2 students. Test the claim at a .025 significance level that the average students per class is more than 41.5 students. Ho H1: Graph of the critical information: Test Statistic: Conclusion based on Ho : Conclusion based on the problem: There sufficient evidence at the significance level to the claim that5. The State Office of Higher Education reports that the average age at graduation for graduates from all community colleges in the state is 25.7 years old. The Vice President of Instruction feels that this is not true for Folsom Lake students. She feels that the average age of graduation of FLC students is less than 25.7 years. She directs the college researcher to conduct a random sample of 71 graduates at FLC. The sample has an average age at graduation of 24.1 years with a standard deviation of 2.5 years. Test the claim at a a - .01 significance level that the average age at graduation for FLC graduates is less than 25.7 years. Ho H: Graph of the critical information: Test Statistic: Conclusion based on Ho : Conclusion based on the problem: There sufficient evidence at the significance level to the claim that6. A local connivence store reports to the State Sales Tax Office that that the average daily tax it collects is $ 105.12. The state selects this store to audit based on its claim that the tax should be more than $105.12. The Tax Office audits 31 random daily tax receipts from the store and finds the sample of 31 daily tax receipts has an average of $ 117.82 with a standard deviation of $ 28.45 Test the claim at a a = .01 significance level that the average daily tax collected by the store is not equal to the $ 105.12 that it reports. Ho H: Graph of the critical information: Test Statistic: Conclusion based on Ho : Conclusion based on the problem: There sufficient evidence at the significance level to the claim that