# 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]

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

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]

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

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

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

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

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

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

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

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

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

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

1. If you are unlucky in roulette you should stick with the same number because it has to come up eventually.
2. 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.
3. In the long run we can expect similar numbers of heads and tails from a fair coin.
4. The mean of a large sample will be larger than the mean of a small sample.
5. The standard deviation of a large sample will be smaller than the standard deviation of a small sample.

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

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

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)?

1. 10
2. 0.67
3. 1.5
4. 95
5. -1

10. Which of the following statements is false?

1. Inferential statistics draw upon information from sample data.
2. Inferential statistics draw upon knowledge of how random processes behave.
3. Inferential statistics make statements about samples based on observing populations.
4. 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.
5. Inferential statistics are based on the ratio of information to error.

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

1. Descriptive error.
2. Statical variability.
3. Measurement error.
4. Random error.
5. Random variation.

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?

1. Chance outcome.
2. Expected value.
3. Random event.
4. Random value.
5. Arbitrary outcomes in sampling space.

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?

1. The normal distribution theorem.
2. The central limit theorem.
3. The sampling distribution theorem.
4. The law of large numbers
5. The law of time and relative dimensions in space.

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

1. Standard mean units.
2. z-units.
3. Standard deviation units.
4. Variance units.
5. Zoned units.