# Question

In this exercise, we expect the population mean to be 30 but the mean of our sample is 31. So wouldn’t our null hypothesis be: the sample represents a population of mean 31?

We then go on and use `test_1samp(ages, 30)`

to find the p-value. I am unclear about these steps.

What are we checking for in this hypothesis test? Are we checking If the sample represents a population of mean 30? If so, if it is less than 0.05 then does it mean it represents a population of mean 30?

# Answer

First, let’s note that the null hypothesis is usually the status quo. If we expect that the population mean is 30, *this* is the status quo and this is why our null hypothesis is

The set of samples belongs to a population with the target mean of 30

By performing `test_1samp(ages, 30)`

, we are testing the likelihood that the samples that we have in `ages`

were taken/drawn from a distribution with mean 30. We could of course have just gotten somewhat unlucky with our sampling in this case, especially since the number of samples for `ages`

is small. If the resulting p-value is less than 0.05, we will *reject* the null hypothesis, meaning that we’re saying *it is unlikely* that the sample was drawn from a distribution with mean 30. A p-value greater than or equal to 0.05 means that we *fail to reject* the null hypothesis, meaning that we cannot be confident that the samples *were not* drawn from a distribution with mean 30.