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Chapter 16 – Inference in Practice

Chapter 16 – Inference in Practice. Acceptance Sampling - Accepting or rejecting a sample based on inference ( ex : shipment testing) We still use a Null and Alternate hypothesis: H o : The sample meets standards H a : The sample does not meet standards

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Chapter 16 – Inference in Practice

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  1. Chapter 16 – Inference in Practice • Acceptance Sampling - Accepting or rejecting a sample based on inference (ex: shipment testing) • We still use a Null and Alternate hypothesis: • Ho: The sample meets standards • Ha: The sample does not meet standards • It is possible that our decision will be wrong: • We may reject a good shipment • We may accept a bad shipment • To distinguish between these two errors, we give them special names: • Type I error: If we reject Ho when in fact Ho is true. • Type II error: If we accept Ho when in fact Ha is true.

  2. @  = 0.05 • We describe the performance of a test by calculating probabilities of Type I and Type II errors… • ex: Shipment of bearings: •  = 2.000 cm •  = 0.010 cm • n = 5 • Ho:  = 2 • Ha:  ≠ 2 • z* = 1.96 • Reject if: • Type I error = rejecting the sample when  really is 2. • Type II error needs a limit - we agree that 2.015 is “bad” - if we were to accept a shipment where  = 2.015, we would be making a Type II error.

  3. The probability of a Type I error =  (0.05 in our example…) • The probability of a Type II error must be calculated… • Step 1: Find ‘acceptance limits’: • Step 2: Calculate the probability of accepting Hoassuming that the alternative is true: • Alt- = 2.015 • Standardize acceptance limits using Alt-:

  4. 2nd VARS -1.39 • So we are looking for the area • between z = -5.32 and -1.39 • So this test: • Will reject 5% of all good samples • Will accept 8.23% of samples bad enough that  = 2.015

  5. Power of a Test • Power - The probability that a fixed level  significance test will reject Ho when alt- is true. (which actually is what should happen…) • aka: “The power of the test”… • Power = p-value of acceptance limit vs. alt-OR • Power = (1 - Type II error) • Essentially says what would happen if we repeated the test many times… • Increasing n ( sample size) will increase the power of the test… • Considerations • Significance testing measures the strength of sample evidence against Ho

  6. Not being able to reject Ho does not mean Ho is true - only that the evidence against it is insufficient … • Decision testing forces a choice between 2 hypotheses - we must say that one or the other is supported by the evidence.

  7. HW 5.4 • Vocab pg 397 • #’s 5.69 - 5.71 all

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