Question

Explain how and why the magnitude of a t value affects the probability of rejecting the null hypothesis, for negative and positive numbers.

Answer 1

Whether we use magnitude of t value with or without sign assigned to it in decision of accepting or rejecting null hypothesis depends on the nature of alternative hypothesis as follows.

1. If our alternative hypothesis is of not equal to type , we reject our null hypothesis if , critical value is considered the positive critical value.
2. If our alternative hypothesis is of greater than type , we reject our null hypothesis if , where critical value is always positive in such case.
3. If our alternative hypothesis is of lesser than type , we reject our null hypothesis if , where critical value is always negative in such case.

Now as magnitude of t value increases, the probability of being outside of the confidence interval increases. It goes further beyond critical values and are more prone to be rejected. In this manner, with higher magnitude of t value (both in positive and negative cases) probability of rejecting the null hypothesis increases.