# Hypothesis Testing - Which Condition is More Important

#### BDD

##### New Member
Hello,

I have a question where the sample is n=25, However, the question provides the population mean and the standard deviation.

After several hypothesis questions, part b asks:

Your test in part (a) required two important assumptions in addition to the assumption that the value of is known.
What are they?

I stated:

1 – That a random sample is selected from the target population.
2 – That the distribution of the population is approximately normal. If N>-30, due to the CLT this condition guarantees that the distribution of the population is approximately normal. In this case we are given the population mean and σ.

Which of these assumptions is most important to the validity of your conclusion in part (a)

my original answer was :

It is most important the random sample is selected from the target population. If not, the sample itself will not be representative of the population and the result will likely be invalid. If the distribution is not normal the answer may not be accurate but is at least working with the correct sample data.

I am now thinking it may be more important that the condition 2 - the distribution be normal may be the correct answer? What do you think?

Thanks,

#### obh

##### Member
when you compare means, if the distribution is symmetrical then the test is considered as "robust" to a violation of the normal distribution assumption