Southwest Minnesota State University Department of Business and Public Affairs Fin 230-01: Business Statistics Exam 3 Module 3 due March 31, 2016 at 5PM LeBron and Kyrie Company has a computer controlled machine that is programmed to do precision cutting of a circular brass disc with a mean diameter of 6.125 inches. The shop foreman takes a random sample of 8 discs from the production line. The diameters are as follows: 6.115 6.127 6.129 6.113 6.124 6.121 6.131 6.124 The foremen, Jonathan Johnson and Kevin Parks, suspect that the machine is out of adjustment. Use the hypothesis testing procedure to determine if the programmer needs to make adjustments. Select 0.01 significance level. Step 1: State the null and alternative hypothesis: Null (H0): There is no significant adjustment that is needed to cut a circular brass disc. = 6.125 Alternative (H1): An adjustment must be made in order to fix the machine. M cannot = 6.125 Question: a. Based on step one is this one or two-tail test of hypothesis? Two Tailed Test b. How do you know? Be specific; do not write more than 5 words for this subquestion. Uses = and no direction. Step 2: Select the level of significance; (easy... can miss this question) You select = .01 Question: What does the value of mean? Probability of rejecting a true null hypothesis and making a type 1 error, which is rejecting the null hypothesis when it is true. Dr. Lawrence Muzinga Southwest Minnesota State University Department of Business and Public Affairs Fin 230-01: Business Statistics Step 3: Select the test statistic: Normal Distribution Question: Why did you select that distribution? Please do not write more than 3 words. Random Sample Step 4: Develop the decision rule: Hint: the decision rule is a statement of the conditions under which the null hypothesis is rejected. State it as it is in the power point. Do no write a paragraph here! Make sure you tell me from this step what is the critical value. The critical values are given in appendix (Table). Find the number of degrees of freedom. Use your answer step 1 (one or two-tailed test), to find the portion of the table labeled (one or two-tailed). Locate the column for the 0.01 significance level. Read down the column until it intersects the row with your calculated degrees of freedom. First step: since this is a two tailed test, half of .01 is .005. .005 is placed at each tail. Decision Rule: Value of Z is not between -2.576 and 2.576 because it would disagree with H0. Degree of Freedom: n-1=8-1=7 (n=sample size) Value = 3.449 Step 5: Make a decision regarding the null hypothesis, and interpret the results: Write down the formula you use here: Here, calculate the mean and standard deviation of the sample. Dr. Lawrence Muzinga Southwest Minnesota State University Department of Business and Public Affairs Fin 230-01: Business Statistics What is your final decision? Do you reject or not reject the null hypothesis? Why? What is your final decision? Do you reject or not reject the null hypothesis? Why? Problem 2: Draw and label the graph that show (1) the rejection region and (2) the area of acceptance of H0. Dr. Lawrence Muzinga