# An Adventure in Statistics: The Reality Enigma

## Student Resources

# Chapter 10: Hypothesis testing

Quizzes are available to test your understanding of the key concepts covered in each chapter. Click on the quiz below to get started.

1. ‘Children can learn a second language faster before the age of 7’. Is this statement:

- A non-scientific statement
- A one-tailed hypothesis
- A two-tailed hypothesis
- A null hypothesis

The correct answer is B. A one-tailed hypothesis. This is because it states the direction of the effect.

2. If my experimental hypothesis were ‘Eating cheese before bed affects the number of nightmares you have’, what would the null hypothesis be?

- Eating cheese before bed gives you more nightmares.
- Eating cheese before bed gives you fewer nightmares.
- Eating cheese is linearly related to the number of nightmares you have.
- The number of nightmares you have is not affected by eating cheese before bed.

The correct answer is D. The number of nightmares you have is not affected by eating cheese before bed. This is because the null hypothesis is the opposite of the alternative hypothesis and so usually states that an effect is absent.

3. If my null hypothesis is ‘Dutch people do not differ from English people in height’, what is my alternative hypothesis?

- Dutch people are taller than English people.
- English people are taller than Dutch people.
- Dutch people differ in height from English people.
- All of the statements are plausible alternative hypotheses.

The correct answer is D. All of the statements are plausible alternative hypotheses. This is because all of the statements state that an effect will be present.

4. Of what is *p* the probability if the null hypothesis were true? (*Hint*: NHST relies on fitting a ‘model’ to the data and then evaluating the probability of this ‘model’ given the assumption that no effect exists.)

*p*is the probability that the results are due to chance, the probability that the null hypothesis (H0) is true.*p*is the probability of observing a test statistic at least as big as the one we have if there were no effect in the population (i.e., the null hypothesis were true).*p*is the probability that the results are not due to chance, the probability that the null hypothesis (H0) is false.*p*is the probability that the results would be replicated if the experiment was conducted a second time.

The correct answer is B. *p* is the probability of observing a test statistic at least as big as the one we have if there were no effect in the population (i.e., the null hypothesis were true).

5. A Type I error occurs when: (*Hint*: When we use test statistics to tell us about the true state of the world, we’re trying to see whether there is an effect in our population.)

- We conclude that there is not an effect in the population when in fact there is.
- We conclude that the test statistic is significant when in fact it is not.
- The data we have typed into SPSS is different from the data collected.
- We conclude that there is an effect in the population when in fact there is not.

The correct answer is D. We conclude that there is an effect in the population when in fact there is not. This is because if we use the conventional criterion then the probability of this error is 0.05 (or 5%) when there is no effect in the population.