Download Hypothesis Testing for One Man - Homework for Practice | STAT 4706 and more Study notes Statistics in PDF only on Docsity! STAT 4706 HW # 4 CHAPTER 10 & 16 – HYPOTHESIS TESTING FOR ONE MEAN, SAMPLE SIZE AND POWER NOTES Due Tuesday September 20th at 3:30pm NOTE: YOU WILL NOT RECEIVE THIS HOMEWORK BACK BEFORE THE FIRST EXAM. MAKE A COPY OF YOUR HOMEWORK SUBMISSION TO COMPARE TO THE SOLUTIONS IN ORDER TO PREPARE FOR THE EXAM. 1) Explain why a null hypothesis for a hypothesis test for the mean will never have the symbol “x-bar” in it. 2) A manager at a manufacturing plant wants to investigate the quality of his employees’ work after one employee says that he thinks some of the other employees need retraining. The manager has been saying that the average number of acceptable parts coming from their department is 90%. He collects data over a two-week window on 100 employees to test if the number of acceptable parts is less than 90% at a .05 level of significance. If it is less than 90%, he feels compelled to implement a re-training program. The data is in HW4_1.xls. a) Use JMP to obtain the mean and standard deviation of the number of acceptable parts. Identify these values using the correct symbols. b) Make an argument as to which type of test we should use: parametric vs. non-parametric. c) Use JMP to conduct the appropriate hypothesis test. Include output with the solution. (Write out hypotheses, test statistic, p-value, decision and conclusion.) d) Explain what a type I and type II error would be in terms of implementing a re-training program and whether the program is actually needed. 3) A food inspector examines 16 jars of a certain brand of jam to determine the percent of foreign impurities. The following data were recorded. 2.4, 2.3, 3.1, 2.2, 2.3, 1.2, 1.0, 2.4, 1.7, 1.1, 4.2, 1.9, 1.7, 3.6, 1.7, 3.6, 1.6, 2.3 a) Make an argument as to which type of test we should use: parametric vs. non-parametric. b) Use JMP to determine if the average percent of foreign impurities is greater than 2.5%. (Write out hypotheses, test statistic, p-value, decision and conclusion.) 4) Holding all other things constant (population mean, sample mean and variance), increasing the sample size results in a) a larger test statistic b) a smaller test statistic c) no change in the test statistic value. 5) Is the following statement true or false? Explain your response. A larger test statistic (in terms of absolute value….treat t = -4 as being as large as t = 4)makes it more likely that we will Fail to Reject H0. 6) What sample size is needed if we want the power of our t-test to be .90 if it is essential to detect a difference of a half of a standard deviation for a one-tailed test? 7) Use JMP to create a power curve for differences and sample size if we have a standard deviation of 10. a) Use the curve to approximate the sample size needed to obtain a power of .75. b) Use the curve to approximate the sample size needed to obtain a power of .90.
