# Answers to the checkpoints of chapter 5

Checkpoint 1

•  When it is unbiased, it is valid and accurate; when it is accurate, it is reliable (consistent) and the distribution is narrow.
• It affects the “validity.”
• It affects the accuracy.
• Invalid research can still be reliable (consistently missing the target).

Checkpoint 2

• You can estimate the population mean, the population standard deviation and the population proportion.
• You can estimate the mean and the proportion in a population based on the sample mean and the sample proportion.
• For a large number of draws (large sample, repeating experiments) the distribution of a variable is approximated by the normal distribution.
• By having a larger sample.
• The standard deviation of the sample mean.

Checkpoint 3

• Area within which it can be assumed with …% certainty that the actual value falls within this area.
• With a 99% confidence level.
• With small sample sizes (less accurate).
• With a large standard error (less accurate).
• The same mean: all symmetrical with the same center/curve.
Different distribution: each shape is different, from low and wide to high and narrow. Whereas the midpoint is the same for all of them, the distribution is clearly different.

Checkpoint 4

• A confidence interval based on the t distribution.
• For a sample larger than 120.
• The ∞ refers to “infinity.” That is the point from where the t and z distributions approach each other.
• The standard error is the spread of the sample distribution, i.e. the standard deviation divided by the square root of n.

Checkpoint 5

• A hypothesis is an expectation about the results of variables in your population, for instance, there is or is not difference, correlation or effect.
• This is a null hypothesis.
• Inductive statistics involves using sample analyzes to draw conclusions about the population. Another term for this is “inferential statistics.”

Checkpoint 6

• This is also known as the significance level.
• If p = 0.03 in a one-tailed test, we reject the null hypothesis.
• In a two-tailed test, p < ½ α. So 0.03 < 0.025. That is not the case, so the hypothesis is not rejected.
• There is a difference (no direction).

Checkpoint 7

• The extent to which you reject null hypotheses that are not true, i.e. rejecting them is justified.
• Under hypothesis
H0: The woman is not pregnant
H1: The woman is pregnant
Type II: the pregnancy test says she’s not pregnant, when in fact she is.
Type I: the pregnancy test says she’s pregnant, when in fact she is not.
• Reliability of a test is the chance that H0 will not be rejected because H0 is true.
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