Steps for Calculating for a Large-Sample Test about µ2.Specify the value of µain the alternative hypothesis for which the value of is to be calculated. Then convert the border value(s) of to z-value(s) using the alternative distribution with mean µa. The general formula for the z-value iszx0axx0
Steps for Calculating for a Large-Sample Test about µSketch the alternative distribution (centered at µa) and shade the area in the acceptance (nonrejection) region. Use the z-statistic(s) and Table II in Appendix D to find the shaded area, which is .
Power of Test•Probability of rejecting false H0•Correct decision•Equal to 1 – •Used in determining test adequacy•Affected by•True value of population parameter•Significance level •Standard deviation & sample size n
Two-Tailed zTest Example Does an average box of cereal contain at least 368grams of cereal? A random sample of 25boxes had x= 372.5. The company has specified to be 15grams. Test at the .05level of significance.368 gm.
Properties ofand Power1.For fixed nand , the value of decreases, and the power increases as the distance between the specified null value µ0and the specified alternative value µaincreases.
Propertiesof andPower2.For fixed nand values of µ0and µa, the value of increases, and the power decreases as the value of is decreased.
Properties of and Power3.For fixed nand values of µ0and µa, the value of decreases, and the power increases as the sample size nis increased.
Key IdeasKey Words for Identifying the Target Parameter– Mean, Averagep– Proportion, Fraction, Percentage, Rate, Probability 2– Variance, Variability, Spread
Key IdeasElements of a Hypothesis Test1.Null hypothesis (H0)2.Alternative hypothesis (Ha)3.Test statistic (z, t, or 2)4.Significance level ()5.p-value6.Conclusion
Key IdeasErrors in Hypothesis TestingType I Error= Reject H0when H0is true(occurs with probability )Type II Error= Accept H0when H0is false(occurs with probability )Power of Test= P(Reject H0when H0is false)= 1 –
Key IdeasForms of Alternative HypothesisLower-tailed : Ha: < 50Upper-tailed : Ha: > 50Two-tailed : Ha: ≠ 50
Key IdeasUsing p-values to Decide1.Choose significance level ( )2.Obtain p-value of the test3.If > p-value, reject H0