Question

1. How do we determine if we reject or fail to reject a null hypothesis?
2. What are the key pieces needed when writing a conclusion?

Answer 1

#1) There are two approaches to make decision about the rejection of H₀

Critical value approach :

For left tail test , if test statistic is less than the critical value , then reject H₀, otherwise fail to reject H₀.

Do not reject HO Rejection region of Ho critical value

For right tail test , if test statistic is greater than the critical value , then reject H₀, otherwise fail to reject H₀.

Do not reject HO Rejection region of HO Critical value

For two tail test , if test statistic is fall outside the critical values , then reject H₀, otherwise fail to reject H₀.

Do not reject HO Rejection region of HO Rejection region of HO Critical value critical value

P- value approach :

After finding the p- value of the test ,we use the following decision rule to make decision about rejection of H₀

Decision rule :
Reject H₀, if p-value (≤ ) less than or equal to α.
Or Do not reject H₀, if p-value (>) greater than α.

#2) When we reject the H_0, on the basis of critical value or p- value approach, we supposed to accept alternative hypothesis Ha which is based on the claim or hypothesis made by the researcher, so we can conclude that there is sufficient evidence to support the claim.

When we do not reject the H₀, on the basis of critical value or p- value approach, we supposed to accept null hypothesis H₀which is counter or opposite to the claim or hypothesis made by the researcher, so we can conclude that there is no sufficient evidence to support the claim.

For example :

Claim : average score of the class is greater than 60

So H₀ : Average score of the class is equal to 60 or µ = 60

H_a : Average score of the class is greater than 60 or µ > 60

If we rejected the H_0, on the basis of critical value or p- value approach, we supposed to accept alternative hypothesis Ha that average score of the class is greater than 60 ,so we can conclude that there is sufficient evidence to support the claim.

If we do not reject the H₀, on the basis of critical value or p- value approach, we supposed to accept null hypothesis H₀  average score of the class is equal to 60 , so we can conclude that there is no sufficient evidence to support the claim.