Hypothesis Tests

Question 1

What is the central limit theorem?

Answer 1

It’s that sort of magical thing where you theoretically repeatedly sample the original population and calculate the mean for each sample. The distribution of these sample means will follow a normal distribution.

Question 2

What do we need in order for the central limit theorem to apply (use a z-test)?

Answer 2

Either we need n>30

or if not, we need to for magical reasons already know the true population variance.

Question 3

When do we use a t-test for a single mean?

Answer 3

When we want to check the hypothesis that the mean is equal to some specific value BUT the sample size is less than 30 and we don’t know the true population variance.

Question 4

What is an assumption we make when doing a t-test?

Answer 4

That the underlying population is normally distributed.

Question 5

When doing a t-test, do you use the biased or unbiased estimator for the sample standard deviation?

Answer 5

You must use the unbiased estimator (S_n-1)

Question 6

How do you convert between the biased and unbiased sample standard deviation?

Answer 6

Question 7

Which test should I use if I want to prove that a mean is 50?

Answer 7

• z-test for the mean
• t-test for the mean

Question 8

How do we use the p-value to make a conclusion about a hypothesis test?

Answer 8

If the p-value is less than the significance level, we reject H0.
Otherwise we fail to reject.