Question

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

Short answer

The null hypothesis would be rejected for every case except the last one because the given p-values are greater than the value in the last one.

Step-by-step solution

General rule for each case

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.

Finding whether the null hypothesis will be rejected or not for part a.

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

Finding whether the null hypothesis will be rejected or not for part b.

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.

Finding whether the null hypothesis will be rejected or not for part c.

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.

Finding whether the null hypothesis will be rejected or not for part d.

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.

Finding whether the null hypothesis will be rejected or not for part e.

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.