Download Statistics Exam: Hypothesis Testing and Confidence Intervals and more Exams Mathematics in PDF only on Docsity! Page 1 of 4 Statistics 150: Introduction to Statistics Exam 3 - Chapter 8, 9.1, 9.2 November 17, 2000 Name: ____________________________________ Section 1 Directions: This section contains five computational problems worth a total of 85 points. For each problem, you must present all your work, as well as the final answer, in order to receive full or partial credit. 1. Vitamin B6 is one of the vitamins in a multiple vitamin pill manufactured by a pharmaceutical company. The pills are produced with a mean of 50 mg of vitamin B6 per pill. The company believes that there is a deterioration of 1 mg per month, so that after three months they expect the mean to be 47 mg. However, a consumer group suspects that actual mean will be less than 47 mg. In search of the truth, the consumer group conducted an experiment where the actual amount of vitamin B6 was measured for a random sample of 50 three-month-old pills. The result yielded a mean of 46.94 mg with a standard deviation of 0.15 mg. What should the consumer group conclude with the Type I error rate of .05? (a) State the null and alternative hypotheses. (4 pts.) (b) Perform an appropriate test and draw a conclusion. (10 pts.) (c) Compute the p-value of the test. (6 pts.) (d) Assuming that the true mean amount of vitamin B6 after three months is 46.93 mg, compute the power of the test. (10 pts.) Page 2 of 4 2. A company that produces cereal claims that its “10-oz. box” has a mean net weight of 10.2 oz. In order to test the truth of the claim, twenty-seven 10-oz. boxes were purchased from a variety of grocery stores and their net weights were measured. The obtained data were analyzed using MINITAB, the results of which are presented below. T-Test of the Mean Test of mu = 10.2000 vs mu not = 10.2000 Variable N Mean StDev SE Mean T P Weight 27 10.1870 0.2132 x.xxxx -0.32 0.75 (a) In the MINITAB output, the value for “SE Mean” (standard error of the mean) has been erased. Recover that value using the relevant information found in the output. (5 pts.) (b) With an alpha level of .05, what would you conclude about the company’s claim? Show your reasoning. (Note: Answer this question in reference to the p-value presented in the output.) (6 pts.) 3. It was claimed that 75% of all dentists recommended a certain brand of gum for their gum- chewing clients. However, a consumer group suspected that this percentage was too high and, thus, decided to conduct a test. A survey of 390 dentists found that 273 recommended this brand of gum. What should the consumer group conclude? Use α = .01. (a) State the null and alternative hypotheses. (4 pts.) (b) Perform an appropriate test and draw a conclusion. (You need not compute the p-value.) (10 pts.)
