1. Large samples may detect even “small departures” from  as being statistically significant.
2. Statistical significance is much harder to achieve with small samples. Therefore, even when is false, it may be the case that you will rarely reject it if you always have to use small sample sizes.
Example: A machine designed to fill cans of corn is supposed to be calibrated so that the mean fill weight is 12 oz. Let  denote the true mean fill weight, and assume the standard deviation of weight is 0.20 oz. A sample of 100 cans has a sample mean of 12.04 ounces.
a) Decide at 5% significance whether or not the machine is calibrated correctly.
b) Find a 95% confidence interval for .
Solution:
a) i) The test is TTA:  vs 
ii) The test statistic is 
iii) The p-value is 
iv) The p-value is (barely) below 5%, so we (barely) reject the null hypothesis
Conclusion: The machine is not calibrated correctly
b) 
The Relationship between CIs and TTA tests
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