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tutorial07-F09w

tutorial07-F09w - ISMT 111 L1 BUSINESS STATISTICS TUTORIAL...

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1 ISMT 111 L1 B USINESS S TATISTICS T UTORIAL 7 created by Andrew Yam Definition Null Hypothesis ( 0 H ) - a hypothesis we assume to be TRUE, e.g. 0 0 : m m = H - assumption we wish to test Alternative Hypothesis ( a H or 1 H ) - a hypothesis we wish to support, e.g. 0 : m m a H - conclusion when we reject 0 H Observed Test Statistics ( obs z or obs t ) - a value used to make the decision, e.g. n X z obs / 0 s m - = 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 0 H than the observed value - the smallest value of a to reject 0 H , e.g. ( 29 obs z z P Type I and Type II Error Type I error: reject 0 H when it is TRUE. P(committing Type I error) = P(reject 0 H | 0 H is true) = a Type II error: do not reject 0 H when it is FALSE. P(committing Type II error) = P(not reject 0 H | 0 H is false) = b

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2 0 H is TRUE 0 H is FALSE Reject 0 H Type I error a (Significance Level) b - 1 (Power of the Test) Do NOT Reject 0 H a - 1 (Confidence Coefficient) Type II error b Note: - For fixed n , ↑⇒ b a and ↓⇒ b a - ↑⇒ b a and n Hypothesis Testing of a Population Mean, m Null Hypothesis, 0 0 : m m = H z -test (Large Sample) - Normal Population; s is known - OR Non-normal Population; unknown s ; but large sample size n Test Statistics: n X z obs / 0 s m - = i) 0 : m m < a H , 0 H is rejected when a z z obs - < , ii) 0 : m m a H , 0 H is rejected when a z z obs , iii) 0 : m m a H , 0 H is rejected when 2 / a z z obs - < or 2 / a z z obs . Note: - When n is large, unknown s can 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)