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Hypotheses%20testing%20based%20on%20a%20single%20sample

# Hypotheses%20testing%20based%20on%20a%20single%20sample -...

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Click to edit Master subtitle style 4/24/11 Hypotheses testing based on a  single sample

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4/24/11 Statistical hypotheses  Statistical Hypothesis  is a claim or assertion  about the value of one or more population  parameters.  Null Hypotheses H0:  Put here what is  typical  of the population, a  term that characterizes “no change”. Alternative Hypotheses H1:  Put here what is the  challenge , the view of  some characteristic of the population that, if it were
4/24/11 Beginning an Example When a robot welder is in adjustment, its  mean time to perform its task is 1.3250  minutes. Past experience has found the  standard deviation of the cycle time to be  0.0396 minutes. An incorrect mean operating  time can disrupt the efficiency of other  activities along the production line.  For a  recent random sample of 80 jobs, the mean  cycle time for the welder was 1.3229 minutes.

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4/24/11 Building Hypotheses What decision is to be made? The robot welder is in adjustment. The robot welder is not in adjustment. How will we decide? “In adjustment” means  µ  = 1.3250 minutes. “Not in adjustment” means  µ    1.3250 minutes. Which requires a change from business as usual?  What  triggers new action?
4/24/11 Types of Error No error Type II error: β Type I error: α No error State of  Reality H0 True H0 False Do not Reject H0  Reject  H0  Tes Say s

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4/24/11 Types of Error Type I Error: Saying you reject H0 when it really is true. Rejecting a true H0. Type II Error: Saying you do not reject H0 when it really is false. Failing to reject a false H0.
4/24/11 The Null Hypothesis Nondirectional, two-tail test: H0: pop parameter = value Directional, right-tail test: H0: pop parameter   value Directional, left-tail test: H0: pop parameter   value    Always put hypotheses in terms of population parameters.

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4/24/11 Acceptable Error for the Example Decision makers frequently use a 5% significance  level.  Use  α  = 0.05. An  -error means that we will decide to adjust the machine  when it does not need adjustment. This means, in the case of the robot welder, if the machine is  running properly, there is only a 0.05 probability of our  making the mistake of concluding that the robot requires  adjustment when it really does not.
4/24/11 Nondirectional, Two-Tail Tests H0: pop parameter = value H1: pop parameter   value

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4/24/11 Directional, Right-Tail Tests  H0: pop parameter   value H1: pop parameter > value
4/24/11 Directional, Left-Tail Tests H0: pop parameter   value H1: pop parameter < value

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Hypotheses%20testing%20based%20on%20a%20single%20sample -...

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