# Research Methods and Statistics in Psychology

## Student Resources

# Chapter 7: Some Principles of Statistical Inference

1. Imagine a coin-tossing experiment in which a coin is tossed 10 times and the researcher records the number of heads obtained. Which of the following statements is true? [TY7.1]

- The binomial distribution helps provide a statistical model for this coin-tossing experiment.
- The binomial distribution gives the probability that the coin is biased.
- Very rare events are always random.
- The information term of the statistic used in this experiment will be a measure of chance, or random error.
- Both (a) and (b).

**Answer:** A

2. Jane has an IQ of 145. The area beyond a *z-*score of 3.0 (the *z-*score associated with her IQ) is .001. If we took a random sample of 1000 people from the population (that is known to have a mean of 100 and a standard deviation of 15) then which of the following statements is true? [TY7.2]

- Jane’s
*z*-score will be 3.0. - We can expect about 1 person in the sample of 1000 to have an IQ the same as or higher than Jane’s.
- Both (a) and (b).
- Jane’s
*z*-score is obtained by dividing the binomial distribution by the error term. - Both (a) and (d).

**Answer:** C

3. Which of the following is true of the sampling distribution of the mean? [TY7.3]

- It is an observed distribution of scores.
- It is a hypothetical distribution.
- It will tend to be normally distributed with a standard deviation equal to the population standard deviation.
- The mean will be estimated by the standard error.
- Both (b) and (c).

**Answer:** B

4. Which of the following statements about descriptive uncertainty and inferential uncertainty is true? [TY7.4]

- Both are types of statistical uncertainty.
- Only descriptive uncertainty is a form of statistical uncertainty.
- They are unrelated.
- Both are measured by the information term of any statistic.
- They provide different answers to the same questions.

**Answer:** A

5. Which of the following statements about *z**-*scores is true when they are used to make inferences about individual scores? [TY7.5]

- They are produced by random processes.
- They are calculated by dividing the difference between the score and the mean by the standard deviation.
- They can only be used to make inferences about groups.
- They follow the central limit theorem.
- None of the above.

**Answer:** B

6. Which of the following statements about statistical inferences in psychology is *false? *[TY7.6]

- Statistical inferences usually involve calculating a statistic that is obtained by dividing an information term by an error term.
- Statistical models allow us to calculate the probability that our results are due to chance.
- The sampling distribution of the mean is a useful concept for making inferences about groups.
- Statistical inferences about the mean can often make use of the
*z-*distribution when the population standard deviation is known. - The law of large numbers implies that, other things being equal, it is easier to be confident when making inferences using large samples.

**Answer:** B

7. Which of the following follows from the law of large numbers? [TY7.7]

- If you are unlucky in roulette you should stick with the same number because it has to come up eventually.
- The mean of a small random sample of the population is more likely to be a reliable estimate of the population mean than that of a large sample.
- In the long run we can expect similar numbers of heads and tails from a fair coin.
- The mean of a large sample will be larger than the mean of a small sample.
- The standard deviation of a large sample will be smaller than the standard deviation of a small sample.

**Answer:** C

8. If a set of responses is normally distributed, which of the following statements is **not** true?

- The scores will be symmetrically distributed around the mean
- We can predict the percentage of responses falling within one standard deviations of the mean
- About 95% of responses fall within two standard deviations of the mean
- The mean is a good measure of central tendency
- The data needs to be transformed to satisfy the assumptions of most statistical analyses.

**Answer:** E

9. If a student has an IQ of 90, how many standard deviation units is this away from the mean (note that IQ has a mean of 100 and a standard deviation of 15)?

- 10
- 0.67
- 1.5
- 95
- -1

**Answer:** B

10. Which of the following statements is **false**?

- Inferential statistics draw upon information from sample data.
- Inferential statistics draw upon knowledge of how random processes behave.
- Inferential statistics make statements about samples based on observing populations.
- Inferential statistics are used to make statement about how plausible it is that a random process could have produced results as extreme as those obtained in a given piece of research.
- Inferential statistics are based on the ratio of information to error.

**Answer:** C

11. “The amount of *descriptive uncertainty *or *chance *variation associated with statistical statements and observations.” What is this a glossary definition of?

- Descriptive error.
- Statical variability.
- Measurement error.
- Random error.
- Random variation.

**Answer:** D

12. “The mean value of a probability distribution. For example, this is 25 for the number of heads when a fair coin is tossed 50 times.” What is this a glossary definition of?

- Chance outcome.
- Expected value.
- Random event.
- Random value.
- Arbitrary outcomes in sampling space.

**Answer:** B

13. “The statistical theorem that for large samples the sampling distribution of the mean will be approximately normally distributed.” What is this a glossary definition of?

- The normal distribution theorem.
- The central limit theorem.
- The sampling distribution theorem.
- The law of large numbers
- The law of time and relative dimensions in space.

**Answer:** B

14. “The units in which *z-scores *are expressed.” What does this glossary entry define?

- Standard mean units.
*z*-units.- Standard deviation units.
- Variance units.
- Zoned units.

**Answer:** C

15. “A distribution with a mean of 0 and a standard deviation of 1.” What is this a glossary definition of?

- Random test distribution.
- Standard test distribution.
- Mean-centred distribution.
- Random distribution.
- Standard normal distribution.

**Answer:** E