【正文】 these two groups have happened byrandom chance?
Should the engineer switch to the new process?These kinds of problems are veryfamiliar to engineers. An engineer isgiven a task to improve a process orproduct. After a change in the process,the engineer is left with the problem ofdetermining whether the process changehas made a significant improvement ornot. Though engineers often use moreadvanced techniques to determine theimproved settings (DOE, for example, tobe discussed later), a hypothesis test isoften used to verify the experimentresults.The process may be as follows:?Identify the problem.?Design and run an experiment tofind an improved condition.?Analyze the data and determine theimproved operating point.?Verify the effectiveness of theimprovement with a hypothesis test.A Few Illuminating Details
QC data were available for light bulbs produced in the same factory.All of the bulbs had been produced using the standard filamentcoating process. The data was prised of the averages of 10samples from consecutive batches of light bulbs. The engineercalculated the differences between consecutive groups and recordedit in a Minitab worksheet in column QCData.
Considering the new data, the question now bees:“How often has the mean brightness of a groupof light bulbs been 22 lumens brighter than thegroup produced immediately before?”
Open Minitab worksheet for the dataIn the Minitab datasheet, column‘OldData’ is the first set of 10 from theold process.‘NewData’ is the set of data from the newprocess.‘PlantData’ is the 210 averages of 10consecutive measurements from the oldprocess in sample order.‘Diff’ is the magnitude of the differencebetween consecutive groups.What Is a Hypothesis Test?
A hypothesis test is simply paring reality to anassumption and asking, “Are they the same?”O(jiān)r
A hypothesis test is testing whether real data fits a modelOr
A hypothesis test is paring a statistic to a hypothesis 均值測(cè)試:Means Tests1. State the practicalproblem2. State the null hypothesis3. State the alternatehypothesis4. Test the assumptions ofthe data*5. Calculate theappropriate test statistic(or calculate pvalue)6. Lookup the critical valuefrom the appropriatedistribution (or set alpha)7. If the calculated statisticmeets the decision rulecriteria (or if pvalue α )then reject H08. Formulate the statisticalconclusion into apractical solutionThis is the general recipe for hypothesistesting. The tests differ in the appropriatestatistics and appropriate distributions.The means tests recipe is the same as waswhat learned for variance testing.Example – One Mean Vs. Target
Background – A pany audits its stock of tennis balls by testing the bounceheight of 10 randomly selected balls. The average bounce height of thesample is in. The historical data is μ= and σ = . Has storagedegraded the bounce of the tennis balls? Use α = .1. State the practical problem: Is the bounce height of the stored population less than the historicalvalue?2. State the null hypothesis H o : μstored = 3. State the alternate hypothesis H A : μstored 4. Test assumptions: normality of the data pvalue = – Data is normalA very mon test is sampling stockfrom the warehouse for conformity to astandard.This example has a tennis ball panychecking whether the balls in storage stillmeet the bounce specification.Exercise – Mean Vs. Target
Some local farmers believe that this year’ssoybean crop has an exceptionally high yield. Thestatewide average yield for the past five years has been520 bushels/acre with a standard deviation of 117.Thirtysix farms were sampled and。 中心限理論:Central Limit TheoremQ: Why Are So Many Distributions Normal? Why is something thisplicated somon?Science has shown us that variables thatvary randomly are distributed normally. Soa normal distribution is actually a randomdistribution.Another reason why some distributionsare normally distributed is becausemeasurements are actually averages overtime of many submeasurements. Thesingle measurement that we think we aremaking is actually the average (or sum) ofmany measurements. The Central LimitTheorem, discussed in the following slides,provides an explanation of why averages ofnonnormal data appear normal.Dice Demonstration (Integer Distribution)
What does a probability distributionfrom a single die look like?
What is the mean?
What is the standard deviation?
Construct a dataset in Minitab
Select Calc Random Data Integer… from the mainmenu
Generate 1,000 rows of data in C1: Min = 1, Max = 6
Use Minitab’s Graphical Summary routine for analysis
Stat Basic Statistics Display Descriptive Statistics… Minitab Output (Typical)The probability distribution of thepossible outes of the roll of a single dieis obviously nonnormal.A perfect distribution would have hadall six bars exactly equal, but even with10,000 data points, there is still somedifferences in the histogram. If a betterestimate is required, a different data setcould be constructed with exactly equalcounts of each possible oute. Try itand see if the numbers are any different. Sampling a Nonnormal Distribution – Exercise
Each person in the class is to toss a single die sixteentimes and record the data. Calculate the mean and standard deviation of eachsample of sixteen Record the means and standard deviations from eachperson in the class in a Minitab worksheet
Use Minitab’s Graphical Summary routine for analysis Stat Basic Statistics Display Descriptive Statistics…Alternately, a sample of sixteen throwsof the dice can be simulated in Minitab asfollows:Select: Calc Random Data Integer… fromthe main menuGenerate 16 rows of data in C1: Min = 1, Max= 6Analyze the Sample Da