You may recall that Type I and Type II errors are important considerations in in

Question

You may recall that Type I and Type II errors are important considerations in inferential statistics. Obviously, we would like for the probability of a type I error (alpha), and the probability of a type II error (beta) to both be small. For a fixed sample size, the lower we set alpha, the higher is beta, and the higher we set alpha, the lower is beta. So our decision on what value to choose for alpha could be an important one. Usually we choose a signficance level (alpha) between .01 and .10.

Provide two examples of hypothesis tests that you might conduct for business applications. In the first one, give an example where the consequences of a Type I error could be very significant (expensive, potentially catastrophic, etc.) -- so we would want to set a low value for alpha. For your second example, consider a scenario where we might be quite concerned with a Type II error, so we would want to set a relatively high value for alpha in order to minimize the chances of committing a type Type II error.

Explanation / Answer

First example is as follows:

H0: Fire alarms will ring automatically if mean pull of fire alarm is 3.

H1:Fire alarms will ring automatically if mean pull of fir ealarm is different from 3.

Rejecting a true null hypothesis (Type I error) will be catastrophe.

Second example is as follows:

H0:Mean ag efor pre-nursery school is 5.

H1:Mean age for pre-nursery school is different from 5.

Here, if one fails to reject the false null hypothesis, typ eII error will occur.

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