Question

You run a small trucking company that transports goods from Bristol, TN to Winslow, AZ. This trip should take 32 hours and 16 minutes (1936 minutes) if done in accordance with safety regulations. However, you believe that your employees have not been following these rules, because they are completing the trip too quickly. You decide to test your hypothesis. You record the time it takes for your employees to make the trip and record the following results. 6. X- 1736 minutes s 635 n 46 A) State your null and alternative hypotheses B) Carry out the test with α-005, and state your conclusion C) Carry out the test with α-0.01, and state your conclusion D) Does your conclusion change with the change in a?

Answer 1

(a) To perform this two-tail hypothesis test, we use the six-step method. Step1: The null and altenative hypotheses are as follows Ho: 1936 (The population mean is equal to 1936) versus Hi : #1936 (The population mean is not equal to 1936) (b) Step2: We have selected a sample of n 46. We deci de to use a 0.05 Step3: Because ơ is unknown, you use the t-distribution and the t-test statistic We must assume that the population mean are normally distributed. Step4: For a given sample size, n, the test statistic t follows at distribution with n-1 degrees of freedom. The criti cal values of the t distribution with 46-1-45 degrees of freedom The table of t test is obtained by using the excel functiontnv(probabihpi,deg rees of treedom) tinv(0.05,45) - 12.014103 0054s 12.014103 Stap5 The sample mean isX 1736min utes The standard deviation is s- 635 The sample size is n 46 The formula for calculating the t-test statistic is given by 2 1736-1936 V46 -200 635 6.78233 -200 93.62564 -2.13617 -一2.13617 The P - value Approach 2P (t2213617) 21-Pts2.13617)) 2(1-0.98093) 2(0.01907) 0.03814 P - value 0.03814 Since, the P- value-0.03814 < 0.05. We reject the null hypothesis Ho Hence, we conclude that the population mean is not equal to 1936 minutes Step6 Decision Because, the test stati stic is 2.13617> to0s4s2.014103 We reject the null hypothesis Ho Hence, we conclude that the population mean is different from 1936 minutes