Answers to the checkpoints of chapter 5
- 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).
- 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.
- 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.
- 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.
- 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.”
- 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).
- 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.