# Answers to the checkpoints of chapter 6

**Checkpoint 1**

- If there are differences between the sample and test value, and if the sample has a normal distribution.
- The hypothesis is that the age is lower, so the hypothesis has a direction.
- The null hypothesis is not rejected (
*p*value = 0.0668; conclusion*p*> 0.005).

**Checkpoint 2 **

- You would use a
*t*test if the population variance is not known and (in some cases) for small samples. - From 120 onwards, the shape of the
*t*distribution is the same as a normal distribution. - A critical value is the
*t*value or the*z*value associated with the chosen significance level.

**Checkpoint 3**

- If you have two dependent groups and the population variance is unknown.
- Because there is an association in the data that has been collected.
- No.

**Checkpoint 4**

- In terms of whether the population variance is known or not known.
- From
*n*= 120 onwards. - That is a test in which the groups being compared have the same variance.
- At
*df*= 199, the critical*t*value is 1.96; if you perform a*z*test, the critical value is also 1.96, because the sample for this is sufficiently large.

**Checkpoint 5**

- No, you don’t reject it;
*p*= 0.06. - Yes, at 5% with a one-tailed test, you would.

**Checkpoint 6**

- You could adjust the degrees of freedom.
- You have made a Type I error.