# Resolved: alternative hypothesis

in the alternative, how is AOV before -AOV after > 0

it should be lower if the new policy is improving the sales

Hi Doaa!

Thanks for noticing!

You are correct. We'll update the course content very soon.

Best,

Ivan

I took me quite some time to digest this part too.

I think there are a few confusing parts on the notebook 5.3. Paired Sample t-Test.ipynb, too.

**FIRST:**

The null hypothesis is stated as follows:

- H0: µ(AOV_Before) - µ(AOV_After) = 0 ('the mean difference in AOV between the new and old return policy is zero').

**We aim to demonstrate that the new return policy results in a higher AOV. Therefore, we adopt an upper-tailed alternative hypothesis (H1) indicating a positive difference between the two population means:**

- **H1: µ(AOV_Before) - µ(AOV_After) < 0 ('the mean difference in AOV between the new and old return policy is less than zero').**

Furthermore, we set the significance level, alpha, to 0.05.

->

NOTE: If **H1: µ(AOV_Before) - µ(AOV_After) < 0, **shouldn't it mean we use lower-tailed test?

If we opted for upper-tailed test, shouldn't it be :

**H0: µ(AOV_After) - µ(AOV_Before) = 0**

**H1: µ(AOV_After) - µ(AOV_Before) > 0**

Which also more coherent with the code in the notebook:

**ttest_rel(data_after, data_before, alternative= "greater")**

-------------------------------

-------------------------------

**SECOND:**

The **scipy.stats.ttest_rel()** function in SciPy is utilized to execute the paired samples t-test—also known as the dependent or related t-test. This test assesses whether there's a significant difference between the means of two paired or dependent samples.

...

**- **'greater'** checks if the mean of the first sample (a) is greater than that of the second sample (b), implying a positive mean difference. For our hypothesis, 'less' should be selected since we assert that the post-policy mean is greater (therefore, the mean difference is negative).**

Note: again, greater or less?

if we want to use 'less' the code should be:

`ttest_rel(data_before, data_after, alternative= "less")`

right?

CMIIW

Hi David,

Thank you for spotting this mistake. You are right.

The alternative should be as follows:

H1: µ(AOV_After) - µ(AOV_Before) > 0

respectively

H1: µ(AOV_Before) - µ(AOV_After) < 0

Accordingly the relevant line of code should be:

ttest_rel(data_after, data_before, alternative= "greater")

respectively:

ttest_rel(data_before, data_after, alternative= "less")