1ISMT111L1BUSINESS STATISTICS –TUTORIAL 7 created by Andrew YamDefinition❧Null Hypothesis (0H) -a hypothesis we assume to be TRUE, e.g. 00:mm=H-assumption we wish to test Alternative Hypothesis (aHor 1H) -a hypothesis we wish to support, e.g. 0:mm≠aH-conclusion when we reject 0HObserved Test Statistics (obszor obst) -a value used to make the decision, e.g. nXzobs/0sm-=Critical Value (c) -a value used to separate the rejection and non-rejection regions a-the Level of Significance b-1-the Power of the Test p-value -the probability that the test statistic would take a value as or more contradictory to 0Hthan the observed value -the smallest value of ato reject 0H, e.g. (29obszzPType I and Type II Error❧Type I error: reject 0Hwhen it is TRUE. P(committing Type I error) = P(reject 0H|0His true) = a❧Type II error: do not reject 0Hwhen it is FALSE. P(committing Type II error) = P(not reject 0H|0His false) = b
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20His TRUE 0His FALSE Reject 0HType I error a(Significance Level)➼b-1(Power of the Test) Do NOT Reject 0H➼a-1(Confidence Coefficient) Type II error b❧Note: -For fixed n, ↓↑⇒baand ↑↓⇒ba-↓↓↑⇒baandnHypothesis Testing of a Population Mean, m❧Null Hypothesis, 00:mm=H❧z-test (Large Sample) -Normal Population; sis known -OR Non-normal Population; unknown s; but large sample size nTest Statistics: nXzobs/0sm-=i) 0:mm<aH, 0His rejected when azzobs-<, ii) 0:mmaH, 0His rejected when azzobs, iii) 0:mm≠aH, 0His rejected when 2/azzobs-<or 2/azzobs. Note: -When nis large, unknown scan be replaced by s. -Cases i) and ii) are called One-Tailed Test, while case iii) is called Two-Tailed Test. ❧t-test (Small Sample)