In: Statistics and Probability
In hypothesis testing, as the α level gets smaller, the level of confidence increases. T or F, and why or why not?
Ans:
True,Because the level of confidence is: 1 - α , when α is smaller,1 - α increases.
Explanation:
When you set the α level, you are setting the level of random
chance that you are willing to accept.
.
If you set α=.10, then you know that your results could be by
chance 1/10 or 10% of the time.
.
If you set α=.05, then you know that your results could be by
chance 1/20 or 5% of the time.
.
If you set α=.01, then you know that your results could be by
chance 1/100 of 1% of the time.
.
So, it is reasonable to say that your level of confidence in
whether the obtained result is "real" or simply by chance increases
as α is set lower and lower.
.
Note that α itself does not "get smaller." As the statistician, you
set the α level that you want to use. For an initial exploratory
analysis you might use α=.10. For a highly stringent test, you
might use α=.01. Using α=.05 is convention and strikes a balance
between being too aggressive or too conservative.
.