People may have some level of difficulty in making inferences using hypothesis testing.

Let me put forth a common mistake that we do while making conclusions.

We know that when the p-value is less than the level of significance (**α**), we reject the null hypothesis. Commonly we take **α **as 0.05. So when p< 0.05, we reject the null hypothesis.

But, when the p> 0.05 we can not reject the null hypothesis.

At this point, many of us tend to say that ‘**we accept the null hypothesis**‘ and this statement is not correct.

**Reason:**

We make conclusions about the population based on a random chance that could say that Ho is true. But this random chance is at the chosen level of **α**. There is a possibility that some other randomly chosen sample gives a different conclusion at a different level of significance.

**Thus, when p> α, we fail to reject Ho**

When p is greater than α we should write the results in **neutral** language. For example,

Ho: Machine 1 is producing spindles with average length of 30 cm

Ha: Machine 1 is **not **producing spindles with average length of 30 cm

If p< 0.05, At the significance level of 0.05, we reject the null hypothesis that machine 1 is producing spindles with an average length of 30 cm. This also means that we **accept** (and not **prove**) the alternate hypothesis, a nice explanation can be found here for this case.

**When p> 0.05,** at the significance level of 0.05, we can not reject the null hypothesis that machine 1 is producing spindles with an average length of 30 cm.

**This simply means that at a significance level of 0.05, we can not conclude whether the machine is producing an average length of 30 cm or not.**

So, we should always keep in mind that when we are not able to reject the null hypothesis, we should not conclude in any other way but in a neutral manner.

Do share in comments, your experience and other mistakes that you may have once committed/ witnessed.

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