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Hypothesis Tests About With Unknown

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Hypothesis Testing (Revisited) Five Step Procedure 1.Define Opposing Hypotheses. ( ) 2.Choose a level of risk ( ) for making the mistake of concluding something is true when its not. 3.Set up test (Define Rejection Region). random sample 4.Take a random sample. 5.Calculate statistics and draw a conclusion.

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t Statistic in Hypothesis Tests for - ( UNKNOWN) When is known we used: When is unknown we use:

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EXAMPLE Assuming that the ages of MIS managers follow a normal distribution, suppose we wish to draw conclusions about their true mean age (using α =.05) given the following random sample of ages of 5 MIS managers: 25, 30, 32, 38, 25. For this sample:

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EXAMPLE 1: “> TEST” Is there enough evidence to conclude > 27? 1.H 0 : = 27 H A : > 27 2. =.05 3. Reject H 0 (Accept H A ) if t > t.05,4 = 2.132 4. Take Sample: 25, 30, 32, 38, 25 5. We get: There is not enough evidence to conclude > 27.

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EXAMPLE 2: “< TEST” Is there enough evidence to conclude < 35? 1.H 0 : = 35 H A : < 35 2. =.10 3. Reject H 0 (Accept H A ) if t < -t.10,4 = -1.533 4. Take Sample: 25, 30, 32, 38, 25 5. We get: There is enough evidence to conclude < 35.

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EXAMPLE 3: “ TEST” Is there enough evidence to conclude 40? 1.H 0 : = 40 H A : 40 2. =.05 3. Reject H 0 (Accept H A ) if t > t.025,4 = 2.776 or if t < -t.025,4 = -2.776 4. Take Sample: 25, 30, 32, 38, 25 5. We get: There is enough evidence to conclude 40.

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EXCEL t-TESTS For all hypothesis tests, first get the mean and the standard error (s/ n) as follows: Go to DESCRIPTIVE STATISTICS -- Check –Summary Statistics –Confidence Level for Mean (indicate % confidence)

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CHECK -- Summary statistics Confidence Level For Mean

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EXCEL HYPOTHESIS TESTING “> TESTS” Refer to Example 1: H A : >27 Calculate t by: =(Mean-27)/(Standard Error) p-value: if t >0, =TDIST(t,4,1) gives a p <.5 if t.5 Numbers in italics means click on the cell with this value.

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=(B3-27)/B4 =TDIST(E2,4,1) 1-tail test Degrees of freedom t

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EXCEL HYPOTHESIS TESTING “< TESTS” Refer to Example 2: H A : <35 Calculate t by: =(Mean-35)/(Standard Error) p-value: if t <0, =TDIST(-t,4,1) gives a p <.5 if t >0, =1-TDIST(t,4,1) gives a p >.5 Numbers in italics means click on the cell with this value.

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=(B3-35)/B4 =TDIST(-E2,4,1) -t because t < 0 Degrees of freedom 1-tail test

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EXCEL HYPOTHESIS TESTING “ TESTS” Refer to Example 3: H A : 40 Calculate t by: =(Mean-40)/(Standard Error) p-value:=TDIST(ABS(t),4,2) Numbers in italics means click on the cell with this value.

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=(B3-40)/B4 =TDIST(ABS(E2),4,2) To make sure the first argument is >0 Degrees of freedom 2-tail test

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REVIEW t-tests the same as z-tests except: –use s instead of –use t instead of z Excel –Use Descriptive Statistics to get sample mean and standard error –Use of TDIST function

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