Objective:Going down the DMAIC road, you and your team are continuing to tryto get a handle on what is causing additional defects in theleveler plates. You are trying to reduce the variation in that process.There are three test sites that are designed to detect both Type A and Type B defects.People have suggested that the number of Type A or B defects detected depends onwhich test site is doing the testing. In other words, one or more of the test sitesmay not be using the same criteria, method, etc. to detect Type A or B defects and thisis causing the defect rate to be reported inconsistently across the three sites.You have been asked to test the defect rates from the three test sites and settle the debate.One way to find out is through the use of the Chi-Square test for independence.Test at 95% confidence.Chi SquareInstructions for you:We highly recommend working through the practice example in yellow belowbefore tackling this deliverable.1. State the practical problem.2. State the null and alternate hypotheses.3. Compute the chi-square statistic.4. Determine the chi-square critical value.5. What conclusions can you draw?"Hypothesis statement?""Write-up my conclusion?"Sample Exercise in shaded area (not required, but helpful)See manufacturing project assignment data in blue below this exampleSome help for you using an practice example:You first need to calculate the expected values. It is best to makea table as step 1. For example, males and females watch variousTV stations. Let’s say that we want to find out if gender is dependentor independent of television station preferences.The practice data follows:WKBWWBENWGRTotalsMales625425141Females445015109Totals10610440250Step 1. Calculate each of the ‘expected values.’ We will dothe first two for you.a. Probability of viewer being male is 141 / 250 = 0.564(refer to the cells in the table above)b. Probability of viewer preferring WKBW is 106 / 250 = 0.424c. Probability of viewer preferring WKBW AND being maleis 0.564 x 0.424 = 0.239d. Expected number of viewers in this cell is 0.239 x 250 = 59.8etc…a. Probability of viewer being female is 109 / 250 = 0.436b. Probability of viewer preferring WKBW is 106 / 250 = 0.424c. Probability of viewer preferring WKBW AND beingfemale is 0.436 x 0.424 = 0.185d. Expected number of viewers in this cell is 0.185 x 250 = 46.3etc…Repeat this for all six cells. To check your work, the totals(across and down) should add up very close to the (across andand down) totals of the observed values. Here is how yourchart should appear when finished: The ‘expected valuesare in [brackets.]WKBWWBENWGRTotalsMales62 [59.8]54 [58.8]25 [22.5]141Females44 [46.3]50 [45.3]15 [17.5]10910610440250TotalsStep 2. Compare the OBSERVED [EXPECTED]Example: For the first cell (Males/WKBW), the formula is:Observed minus [Expected] Squared divided by [Expected] as follows:(62-59.8)2 divided by 59.8 = 0.0809For the 2nd value…(54-58.8)2 divided by 58.8 = 0.3918For the 3rd value…(25-22.5)2 divided by 22.5 = 0.2778For the 4th value…(44-46.3)2 divided by 46.3 = 0.1143For the 5th value…(50-45.3)2 divided by 45.3 = 0.4876For the 6th value…(15-17.5)2 divided by 17.5 = 0.3571Step 3. Add those chi-square values and you should get 1.7095This is your calculated chi-square statistic.Step 4. Determine the significance level. (e.g., .05 or .01 or .1)This is up to the discretion of the team and the team’s choice is basedupon what level of risk they are willing to live with.Step 5. Determine the Degrees of Freedom (df) for the rows andthe columns. You will need this to find the critical value inthe table in the textbook.df=(number of rows minus 1) multiplied bythe (number of columns minus 1) So, in this particularcase it would be (2-1 multiplied by 3-1) = 2Step 6. Go to the chi-square table in a textbook and determinethe critical value. You already knowthe calculated statistic (1.7095). All you need now is that criticalvalue to see if the calculated statistic is greater than that criticalvalue. If it is greater than the critical value, you can reject thenull. If not, then you fail to reject the null.Data:Data for this deliverable:Site 1Site 2Site 3Defect Type A887Defect Type B9108How to submit an AssignmentProject:Manufacturing 2015Chi SquareDeliverable:Student last name:KimState the null hypothesis:State the alternative hypothesis:Chi Square statistic: (Use 6 decimal places.)CheckCritical value:CheckState your bottom-line conclusion in the words of the problem addressed by this study. HINT: Whatwould you say to your sponsor? (Do not use generic hypothesis testing terms.)Type your bottom-line conclusion in the words of the problem here. Do not use generichypothesis testing terms.To send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COURSE MENU2. CLASS ROSTER3. Click on your instructor’s email envelope iconHINT!4. Type "Check My Work – Chi Square" in the SUBJECT box.5. Click once inside of the message box6. Do a CTRL-V. This will paste your deliverable into this box.Don’t be concerned if after you paste it, the appearance of the text is out ofalignment. It will straighten out after you hit SEND.7. SEND Check your SENT ITEMS folder afterward to see how it straightened out.Please ‘hand-in’ your assignments throughout the course.DO NOT SAVE THEM FOR THE END.Procrastinators: The deadline for having all project deliverables 100% correctis 7 days prior to the end of the course.