Question

true or false:

1) if alpha is made more stringent, beta increases

2) if a result is statistically significant, it must be an important result

3) by using a stringent alpha level and designing the experiement for high power, we maximizes the probability of correctly concluding regardless of whether H0 is true or false

Answer 1

1) if alpha is made more stringent, beta increases - True
Explanation

When we increase alpha we increase the probability of rejecting a true hypothesis.
This inturn decreases the beta which the probability of retaining a false hypothesis. Hence it increases the power of test t. Therefore by making alpha more stringent, the power goes down and beta increases.

2) if a result is statistically significant, it must be an important result - True

When we say a result is statistically significant we mean that the result is not attributed to random chance. Hence the result is important statistically.

On the other, the practical aspect also must be check if the conjecture makes sense in the context.

3) by using a stringent alpha level and designing the experiment for high power, we maximize the probability of correctly concluding regardless of whether H0 is true or false

True.