For each $\alpha$and observed significance level (p-value) pair, indicate whether the null hypothesis would be rejected.

a.$\alpha =0.5,p-value=.10$

b.$\alpha =0.10,p-value=.05$

c.$\alpha =0.01,p-value=.001$

d.$\alpha =0.25,p-value=.05$

e.$\alpha =0.10,p-value=.45$

P-value stands for probability value. It indicates how likely it is that a result occurred by chance alone.

Here, $\alpha$is the level of significance.

If the p-value is less than the level of significance, reject the null hypothesis. Otherwise do not reject the null hypothesis.

a. Given that,$\alpha =0.5$

The p-value is 0.10

Here, the p-value is less than the $\alpha$value.

Therefore, we reject the null hypothesis

b. Given that, $\alpha =0.10$

The p-value is 0.05

Here, the p-value is less than the $\alpha$value.

Therefore, we reject the null hypothesis.

c. Given that,$\alpha =0.01$

The p-value is 0.001

Here, the p-value is less than the $\alpha$value.

Therefore, we reject the null hypothesis.

d. Given that,$\alpha =0.25$

The p-value is 0.05

Here, the p-value is less than the $\alpha$value.

Therefore, we reject the null hypothesis.

e. Given that, $\alpha =0.10$

The p-value is 0.45

Here, the p-value is greater than the $\alpha$value.

Therefore, we do not reject the null hypothesis.