Hypothesis Testing

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• Hypothesis Testing

• Approximate p-value when testing mean of a distribution

• Testing the difference of means of the distribution X̅-Y̅

• Hypo Test 1 (image/png)

• If σ^2 is unknown, replace by its unbiased estimate σ̂^2

• Hypo Test 2 (image/png)

• Hypo Test 2a (image/png)

• Hypo Test 2b (image/png)

• Hypo Test 3 (image/png)

• Hypo Test 4a (image/png)

• Hypo Test 4b (image/png)

• Hypo Test 5a (image/png)

• Hypo Test 5b (image/png)

• Hypo Test 6a (image/png)

• Hypo Test 6b (image/png)

• Hypo Test 7 (image/png)

• Hypo Test 8 (image/png)

• If σ^2 is unknown, replace with σ̂^2;

• Hypo Test 9 (image/png)

• Hypo Test 10 (image/png)

• Remember ranges for rejecting p-value

• Hypo Test 11 (image/png)

• p<0.01     -  very strong evidence to reject0.01<p>0.05    -  strong evidence to rejectp>0.05     -  insufficient evidence to reject

• with p-value;

• or

• where