Question

A researcher did a one-tailed hypothesis test using an alpha level of .01, H0 was rejected.A colleague analyzed the same data but used a two-tailed test with α=.05, H0 was failed to reject. Can both analyses be correct? Explain your answer.

Answer 1

Yes Both analysis can be correct.

Prove it by an example :

Null hypothesis : H_o:

Alternate hypothesis : H_a(Two tailed test)

Given
Hypothesized Mean :	1
Sample Mean :	1.2
Population Standard Deviation :	0.4
Sample Size : n	12
Level of significance :	0.05

p-value for two tailed test :

As P-Value i.e. is greater than Level of significance i.e (P-value:0.0834 > 0.05:Level of significance); Fail to Reject Null Hypothesis

For the same data;

The hypothesis is changed to make it into one tailed test.

Null hypothesis : H_o:

Alternate hypothesis : H_a :

p-value for right tailed test :

As P-Value i.e. is less than Level of significance i.e (P-value:0.0417 < 0.05:Level of significance); Reject Null Hypothesis