IET 3403 : Industrial Experimentation NAME: ___________________________ Exam 2 Problem 1 Points Possible Points Earned 2 3 4 5 6 20 20 20 10 10 20 TOTA L 100% 1. Two manufacturing processes are being compared to try to reduce the number of defective products made. During 8 shifts for each process, the following results were observed: Line Line A B 8 8 n 181 187 x 8 5 s Based on a 5% significance level, did line B have a larger average than line A? Step 1: H0 : HA : Step 2: Step 3: Test Statistic: Step 4: Decision Rule: Step 5: Calculation and Decision Reject or Do Not Reject the Ho Meaning: 2. Two manufacturing processes are being compared to try to reduce the number of defective products made. During 8 shifts for each process, the following results were observed: Line Line A B 8 8 n 181 187 x 8 5 s Based on a 5% significance level, did line B have better performance than line A in terms of process variation? Step 1: H0 : HA : Step 2: Step 3: Test Statistic: Step 4: Decision Rule: Step 5: Calculation and Decision Reject or Do Not Reject the Ho Meaning: 3. A nationwide sample of employed men and women were asked whether they were worried about the security of their job. The results were: Men Women Number sampled 500 500 Number worried 360 315 At the 8% level of significance, can we conclude that there is a larger proportion of men that are worried about their job security? Step 1: H0 : HA : Step 2: Step 3: Test Statistic: Step 4: Decision Rule: Step 5: Calculation and Decision Reject or Do Not Reject the Ho Meaning: 4. An experimental surgical procedure is being studied as an alternative to the old method. Both methods are considered safe. Five surgeons perform the operation on two patients matched by age, sex, and other relevant factors, with the results shown. The time to complete the surgery (in minutes) is recorded. At the 5 percent significance level, is the new way faster? Old Way New di di d (d i d ) 2 Way Surgeon 1 36 29 Surgeon 2 55 42 Surgeon 3 28 30 Surgeon 4 40 32 Surgeon 5 62 56 XXXXXXXXXXXXXXXX XXXXXXX sums d sd = Step 1: H0 : HA : Step 2: Step 3: Test Statistic: Step 4: Decision Rule: Step 5: Calculation and Decision Reject or Do Not Reject the Ho Meaning: 5. An entrepreneur was opening a new fitness equipment store and wanted to determine the quantity of each type aerobic equipment she needed to have in inventory. In a previously opened store she opened, historical data showed the following to be monthly sales by machine in terms of percentage of units sold: Treadmill 42% Elliptical 22% Stairmaster 22% Recumbent bike 14% She sold 200 total units in the first month of business with the following distribution: Treadmill 91 Elliptical 35 Stairmaster 47 Recumbent bike 27 * THESE ARE THE OBSERVED VALUES If her expected sales are to match her previous store, did her observed values equal her expected values at a 5% level of significance? *Use and show the 5-step process along with any supporting information. Expected Values Treadmill Eliptical Stairmaster Recumbent Bike 200 x .42 = 84 200 x .22 = 44 200 x .22 = 44 200 x .14 = 28 Step 1: Ho: Ha: Step 2: Step 3: Test Statistic: Step 4: Decision Rule Step 5: Calculation and Decision 2 ( ( fo fe )2 )= fe Reject or Do Not Reject the Ho Meaning: 6. You believe there is a difference in the attendance of employees in different departments you manage. The departments are Engineering, Human Resources, Product Management, and Manufacturing. The number of days missed by the employees in the departments are listed below. Based on the data collected and an statistical significance level of 5%, is there a difference in the days missed in the departments? Engineering 5 4 10 2 9 X2 HR 8 8 X2 PM 10 8 6 8 X2 Mfg 5 5 5 8 6 7 8 7 2 2 X2 Total Tc Nc X2 SSTOTAL= X 2 ((x ) 2 / n) 2 2 SST = ( ((Tc / nc )) (( x ) / N ) = SSE = SSTOTAL - SST = Source of Variation Treatments Error Sum of Squares Total Ho: Ha: = degrees of freedom in the numerator = degrees of freedom in the denominator = FCritical = FCaclulated = Reject or Do not reject the Ho Meaning: Degrees of Freedom Mean Squares F MST/MSE =