MATH 221 Week 6 Homework

1. Question: A consumer analyst reports that the mean life of a certain type of alkaline battery is more than 63 months. Write the null and alternative hypotheses and note which is the claim. 2. Question: An amusement park claims that the average daily attendance is at least 20,000. Write the null and alternative hypotheses and note which is the claim. 3. Question: Type I and type II errors occur because of what issue within the hypothesis testing process? 4. Question: A scientist claims that the mean gestation period for a fox is 50.3 weeks. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? 5. Question: A marketing organization claims that more than 10% of its employees are paid minimum wage. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted? 6. Question: A sprinkler manufacturer claims that the average activating temperatures is at most 131 degrees. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133 degrees. Assume the population standard deviation is 3.3 degrees. Find the standardized test statistic and the corresponding p-value. 7. Question: A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that has a mean caffeine content of 41.5 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, what type of test is this and can you reject the organization’s claim using the test statistic? 8. Question: A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random sample of 61 of these screens has a mean life of 2.6 years. The population is normally distributed with a population standard deviation of 0.88 years. At α=0.02, what type of test is this and can you support the organization’s claim using the test statistic? 9. Question: A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.75 inches. The population standard deviation is assumed to be 0.20 inches. At α=0.05, should the business reject the supplier’s claim? 10. Question: The company’s cleaning service states that they spend more than 46 minutes each time the cleaning service is there. The company times the length of 37 randomly selected cleaning visits and finds the average is 48.2 minutes. Assuming a population standard deviation of 5.2 minutes, can the company support the cleaning service’s claim at α=0.10? 11. Question: A customer service phone line claims that the wait times before a call is answered by a service representative is less than 3.3 minutes. In a random sample of 62 calls, the average wait time before a representative answers is 3.26 minutes. The population standard deviation is assumed to be 0.14 minutes. Can the claim be supported at α=0.08? 12. Question: In a hypothesis test, the claim is µ≤40 while the sample of 40 has a mean of 41 and a population standard deviation of 5.9 from a normally distributed data set. In this hypothesis test, would a z test statistic be used or a t test statistic and why? 13. Question: A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sample of nine professors finds that the mean time in their offices is 6.1 hours each week. With a sample standard deviation of 0.49 hours from a normally distributed data set, can the university’s claim be supported at α=0.05? 14. Question: A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 28 residents in that town has a mean credit card debt of $3590 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported, assuming this is a normally distributed data set? 15. Question: A researcher wants to determine if zinc levels are different between the top of a glass of water and the bottom of a glass of water. Many samples of water are taken. From half, the zinc level at the top is measured and from half, the zinc level at the bottom is measured. Would this be a valid matched pair test?