S Subject Code and Title STAT 2000: Quantitative Analysis Assessment Module 4: Homework questions Additional Information When there is evidence of academic dishonesty, a student will face Misconduct Procedures. Please refer to Torrens policies and procedures in: http://www.torrens.edu.au/about/policies Instructions Answer these questions and problems Chapter 8 Questions and problems 5, 6, 7, 8, 10, 11, 12, 14, 15, 22 5. In a large group of corporate executives, 20 % have no college education, 10 % have exactly 2 years of college, 20 % have exactly 4 years, and 50 % have 6 years. A sample size of 2 (with replacement) is to be taken from this population. Find the sampling distribution of the mean number of years in college of the executives in the sample. 6. Out of 10 pay telephones located in a municipal building, two phones are to be picked at random, with replacement, for a study of phone use. The actual usage of the phones on a particular day is shown in the accompanying table. Number of calls 10 12 16 Number of phones with this number of calls 2 5 3 (a) Find the sampling distribution of the average number of calls per phone in the sample of two phones. (b) Find the variance of this distribution. 7. To demonstrate the central limit theorem, draw 100 samples of size 5 from a random-number table and calculate the sample mean for each of the 100 samples. Construct a frequency distribution of sample means. Do the same for 100 samples of size 10 and compare the two frequency distributions. Does the central limit theorem appear to be working? 8. The accompanying probability density function is a uniform distribution showing that a certain delicate new medical device will fail between 0 and 10 years after it is implanted in the human body. The mean time to failure is m = 5 years, and the standard deviation is s = 2.88 years. Page 1 of 3 (a) Verify that the total area beneath this density function is 1.0. (b) Find the probability that an individual device will fail more than 8 years after implantation. (c) Find the probability that in a sample of n = 36 of these devices, the sample mean time of failure x will be 8 years or less. 10. A type of cathode ray tube has a mean life of 10,000 h and a variance of 3,600. If we take samples of 25 tubes each and for each sample we find the mean life, between what limits (symmetric with respect to the mean) will 50 % of the sample means be expected to lie? 11. The population of times measured by 3-min egg timers is normally distributed with m = 3 min and s = 0.2 min. We test samples of 25 timers. Find the time that would be exceeded by 95 % of the sample means. 12. A light bulb manufacturer claims that 90 % of the bulbs it produces meet tough new standards imposed by the consumer protection agency. You just received a shipment containing 400 bulbs from this manufacturer. What is the probability that 375 or more of the bulbs in your shipment meet the new standards? (Hint: Use the continuity approximation.) 14. Briefly explain the relationship between inferential statistics and sampling. 15. Suppose a town consists of 2,000 people, 1,100 of whom are registered voters. You are interested in how the people in this town will vote on a bond issue. What group constitutes the population? Give an example of a sample from this population. 22. Suppose the mean amount of money spent by students on textbooks each semester is $175 with a standard deviation of $25. Assume that the population is normally distributed. Suppose you take a random sample of 25 students. (a) What is the mean of the sample mean amount spent on textbooks? (b) What is the standard deviation of the sample mean? Page 2 of 3 Chapter 11 Questions and problems 1, 3, 4, 6, 8, 11, 12, 13, 15, 16 1. For each of the following, test the indicated hypothesis. (a) n = 16, x = 1,550, s2 = 12, H0: = 1,500, H1: > 1,500, = 0.01 (b) n = 9, x = 10.1, s2 = .81, H0: = 12, H1: 12, = 0.05 (c) n = 49, x = 17, s = 1, H0: = 18, H1: < 18, = 0.05 3. A population has a variance 2 of 100. A sample of 25 from this population had a mean equal to 17. Can we reject H0: = 21 in favor of H1: 21? Let = .05. 4. Suppose a sample of 15 rulers from a given supplier has an average length of 12.04 inches and the sample standard deviation is 0.015 inches. If is 0.02, can we conclude that the average length of the rulers produced by this supplier is 12 inches, or should we accept H1: 12.00? 6. An advertisement for a brand-name camera stated that the cameras are inspected and that \"60 % are rejected for the slightest imperfections.\" To test this assertion, you observe the inspection of a random selection of 30 cameras and find that 15 are rejected. Construct a test, using .05. 8. The data entry operation in a large computer department claims that it gives its customers a turnaround time of 6.0 h or less. To test this claim, one of the customers took a sample of 36 jobs and found that the sample mean turnaround time was x = 6.5 h with a sample standard deviation of s = 1.5 h. Use H0: = 6.0, H1: > 6.0, and = .10 to test the data entry operation's claim. 11. What is hypothesis testing? Why are we interested in hypothesis testing? In hypothesis testing, is it possible to prove a hypothesis true? 12. What are the types of errors that can be made in hypothesis testing? Which type of error is generally regarded as more serious? 13. For each of the following pairs of hypotheses, explain what the null hypothesis should be. (a) Not guilty versus guilty in a court case. (b) Cage is safe versus cage is unsafe when testing the safety of lion cages. (c) New drug is safe to use versus new drug is unsafe when determining whether the FDA should allow a new arthritis medicine to be sold. (d) New treatment is safe versus new treatment is unsafe when determining whether the FDA should allow a new treatment for AIDS to be used. 15. Compare a one-tailed test with a two-tailed test. Give some examples wherein a one-tailed test is preferable to a two-tailed test. Give some examples wherein a two-tailed test is preferable to a one-tailed test. 16. Briefly explain what is meant by the power of a test. Why is the power of the test important? Page 3 of 3