18) The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths in millimeters recorded. The lengths (in millimeters) are 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. The mean of the sample is 41.5 and the standard deviation is 1.784. If the computed t = -2.913, has there been a statistically significant change in the mean length of the bars? A) Yes, because the computed t lies in the rejection region. B) No, because the information given is not complete. C) No, because the computed t lies in the area to the right of -2.718. D) Yes, because 43 is greater than 41.5. Answer: A Explanation: This is a two-tailed test, a = 0.02, and the population standard deviation is unknown. The sample size is 12, so the degrees of freedom are 12 - 1 = 11 and the critical values of t are -2.718 and 2.718. Based on the sample information, t = - 41.5-43 S = 1.784 = -2.913 12 The t-statistic is less than the critical value of -2.718; therefore, the null hypothesis is rejected. We can conclude there has been a statistically significant change in the length of the bars. Difficulty: 2 Medium Topic: Hypothesis Testing for a Population Mean: Population Standard Deviation Unknown Learning Objective: 10-06 Use at-statistic to test a hypothesis. Bloom's: Analyze AACSB: Reflective Thinking