NU MGSC 2301 - Chapter 9: Hypothesis testing

Unformatted text preview:

Chapter 9: Hypothesis testing1. HypothesisHo: mu= .20 (Null)H: mu not equal .20 (Alternative) (Put conditions to prove here) ex less than mu < 2. Graph1 tail if greater than equal to/less than equal to2 tail both sidesfind Zcrit or Tcrit with tables3. Decision ruleIf test stat z is >1.96 or <-1.96, reject Ho. Otherwise, do not reject.4. Calculate test stat5. Conclusion Reject Ho/Do not reject Ho6. Evidence supports the claim that…/Evidence does not support the claimPop std. deviation known Sample std. deviation known % Pop. Proportion 2 population meansPop std. deviation known Sample std. deviation known % Pop. Proportionz = x) - μ σ √nt = x) - μ s √nz = )p - p √ p(1-p ) √nPoint estimate ,p = x nz = x)1- x) 2_______ √(σ1)1+ (σ2)2 n1 n2t = x)1- x) 2_______ √(s1)1+ (s2)2 n1 n2Point estimator of P when p1=p2=p3 )p = n1p1+n2p2 n1 + n2SUMMARY OF HYPOTHESIS TESTS ABOUTA POPULATION MEAN: σ KNOWN CASESUMMARY OF HYPOTHESIS TESTS ABOUTA POPULATION MEAN: σ UNKNOWN CASESUMMARY OF HYPOTHESIS TESTS ABOUTA POPULATION PROPORTIONNull hypothesisThe hypothesis tentatively assumed true in the hypothesis testing procedure.Alternative hypothesisThe hypothesis concluded to be true if the null hypothesis is rejected.Type I error The error of rejecting H0 when it is true.Type II error The error of accepting H0 when it is false.Level of significance The probability of making a Type I error when the null hypothesis istrue as an equality.One-tailed test A hypothesis test in which rejection of the null hypothesis occurs for valuesof the test statistic in one tail of its sampling distribution.Z values 1 tail 2 tail.05 1.65 1.96.01 2.33 2.58DF: n1 + n2 - 2Point estimate ,p1 = x nStandard Error___________√ )p(1-p)*(1/n1+1/n2)Point estimate ,p2 = x nTest Stat.z = ) p 1 - ) p 2_______________ √ )p(1- )p)*(1/n1+1/n2)Test statistic A statistic whose value helps determine whether a null hypothesis should berejected.p-value A probability that provides a measure of the evidence against the null hypothesisgiven by the sample. Smaller p-values indicate more evidence against H0. For a lower tailtest, the p-value is the probability of obtaining a value for the test statistic as small as orsmaller than that provided by the sample. For an upper tail test, the p-value is the probabilityof obtaining a value for the test statistic as large as or larger than that provided by thesample. For a two-tailed test, the p-value is the probability of obtaining a value for the teststatistic at least as unlikely as or more unlikely than that provided by the sample.Critical value A value that is compared with the test statistic to determine whether H0should be rejected.Two-tailed test A hypothesis test in which rejection of the null hypothesis occurs for valuesof the test statistic in either tail of its sampling distribution.Power The probability of correctly rejecting H0 when it is false.Power Curve A graph of the probability of rejecting H0 for all possible values of the populationparameter not satisfying the null hypothesis. The power curve provides the probabilityof correctly rejecting the null hypothesis.Chapter 10: Inference About Means and Proportions with Two PopulationsESTIMATING THE DIFFERENCE BETWEEN TWO POPULATION MEANSIndependent simple random samples: Samples selected from two populations in such away that the elements making up one sample are chosen independently of the elementsmaking up the other sample.Matched samples: Samples in which each data value of one sample is matched with a correspondingdata value of the other sample.Pooled estimator of p: An estimator of a population proportion obtained by computing aweighted average of the point estimators obtained from two independent samplesChapter 11: Inferences About Population VariancesSUMMARY OF HYPOTHESIS TESTS ABOUTA POPULATION VARIANCESUMMARYOF HYPOTHESIS TESTS ABOUT TWO POPULATION VARIANCESChapter 13: Experimental Design and Analysis of VarianceF value: chart- DFTR (across lower #)- DFE (down)- level of significancek = number of groups (treatments)n= sample sizeHo: mu1=mu2=m3H: At least one is differentSum of squares (SS) Degrees of freedom (DF) Mean Square F valueTreatments Given SSTR k-1 = DFTR MSTR = SSTR DFTRMSTRMSEError Given SSE n-k = DFE MSE = SSE DFETotal SST n-1K=3N = 47Sum of squares (SS) Degrees of freedom (DF) Mean Square F valueTreatments 1200 3-1 = 2 MSTR = 1200 600 2600 = 43.9913.64Error 600 47-3= 44 MSE = 60013.64 44Total 1800 n-1Factor: Another word for the independent variable of interest.Treatments: Different levels of a factor.Single-factor experiment: An experiment involving only one factor with k populations ortreatments.Response variable: Another word for the dependent variable of interest.Experimental units: The objects of interest in the experiment.ANOVA table: A table used to summarize the analysis of variance computations and results.It contains columns showing the source of variation, the sum of squares, the degrees of freedom,the mean square, and the F value(s).Partitioning: The process of allocating the total sum of squares and degrees of freedom tothe various components.Multiple comparison procedures: Statistical procedures that can be used to conductstatistical comparisons between pairs of population means.Comparisonwise Type I error rate: The probability of a Type I error associated with asingle pairwise comparison.Experimentwise Type I error rate: The probability of making a Type I error on at least oneof several pairwise comparisons.Completely randomized design: An experimental design in which the treatments arerandomly assigned to the experimental units.Blocking: The process of using the same or similar experimental units for all treatments.The purpose of blocking is to remove a source of variation from the error term and henceprovide a more powerful test for a difference in population or treatment means.Randomized block design: An experimental design employing blocking.Factorial experiment: An experimental design that allows simultaneous conclusions abouttwo or more factors.Replications: The number of times each experimental condition is repeated in an experiment.Interaction: The effect produced when the levels of


View Full Document

NU MGSC 2301 - Chapter 9: Hypothesis testing

Download Chapter 9: Hypothesis testing
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Chapter 9: Hypothesis testing and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Chapter 9: Hypothesis testing 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?