# An Adventure in Statistics: The Reality Enigma

## Student Resources

# Multiple choice questions

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

1. Complete the following sentence: A small standard deviation (relative to the value of the mean itself)

(*Hint*: The standard deviation is a measure of the dispersion or spread of data around the mean.)

- Indicates that the data points are distant from the mean.
- Indicates that the mean is a poor fit of the data.
- Indicates that data points are close to the mean (i.e. the mean is a good fit of the data).
- Indicates that you should analyse your data with a non-parametric test.

The correct answer is c) Indicates that data points are close to the mean (i.e. the mean is a good fit of the data).

2. Complete the following sentence: A large standard deviation (relative to the value of the mean itself)

(*Hint*: The standard deviation is a measure of the dispersion or spread of data around the mean.)

- Indicates that the data points are distant from the mean (i.e. the mean is a poor fit of the data).
- Indicates that the data points are close to the mean.
- Indicates that the mean is a good fit of the data.
- Indicates that you should analyse your data with a parametric test.

The correct answer is a) Indicates that the data points are distant from the mean (i.e. the mean is a poor fit of the data).

3. Which of the following is true about a 95% confidence interval of the mean:

- 95 out of 100 sample means will fall within the limits of the confidence interval.
- 95 out of 100 confidence intervals will contain the population mean.
- 95% of population means will fall within the limits of the confidence interval.
- There is a 0.05 probability that the population mean falls within the limits of the confidence interval.

The correct answer is b) 95 out of 100 confidence intervals will contain the population mean. This is because if we’d collected 100 samples, calculated the mean and then calculated a confidence interval for that mean, then for 95 of these samples the confidence intervals we constructed would contain the true value of the mean in the population.

4. ‘Children can learn a second language differently before the age of 7 than after.’ Is this statement:

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

The correct answer is d) A two-tailed hypothesis. This is because it is non-directional, it states that an effect will occur, but it doesn’t state the direction of the effect (i.e., whether learning will be faster or slower before the age of 7)

5. What does the assumption of independence mean?

- This assumption means that none of your independent variables are correlated.
- This assumption means that the errors in your model are not related to each other.
- This assumption means that you must use an independent design rather than a repeated-measures design.
- This assumption means that the residuals in your model are not independent.

The correct answer is b) This assumption means that the errors in your model are not related to each other. An easier way to think about this is in terms of scores on the outcome variable being independent, which means that the behaviour of one participant does not influence the behaviour of another.