Is the null hypothesis more likely to be rejected at alpha = 0.01 than alpha = 0.10? As the significance level increases to alpha = 0.10 from alpha = 0.01, which type of error (type I error or type II error) is more likely to occur? What may be done to reduce the likelihood of incurring this error? Why does the significance level, alpha, differ among industries?
To answer this question, you need to understand 1) what alpha means and 2) the types of errors.
1). About alpha: The significance level (called alpha) is the probability of rejecting the null hypothesis GIVEN that the null hypothesis is actually true. So if alpha is higher, then you have a greater probability of rejecting the null hypothesis when it might actually be true.
2) About the types of errors: There are two types of statistical errors. The first is called type I, and it is the probability of rejecting the null hypothesis when it is actually true. This should sound familiar...yes...this is actually alpha! (So another way to define alpha is to say that it's the probability of committing a type I error). The second error is called type II, and it is the probability of failing to reject (retaining) the null hypothesis when it is actually false.
Now, let's apply these concepts to your questions -- ...
This solution contains comprehensive information on the effect of the significance level (alpha) on the likelihood of obtaining a statistical error. The solution provides a definition and description of alpha, type I errors, and type II errors. It then explains the effect of changing the alpha value in terms of type I and type II errors. Finally, it discusses the implications on this relationship for various fields of study that seek to minimize the likelihood of either type of error.