Question 1

Which of the following is true of the normal distribution?
A)It is a theoretical distribution that is rarely seen.
B)"Normal" in normal distribution is statistical term standing for "Non-linear Random Model, Axis Labelled."
C)Both (a)and (b).
D)The normal distribution is broadly useful for creating models of random processes.
E)Both (b)and (d).

Accepted Answer

The normal distribution is a widely used theoretical distribution that is commonly observed in many natural and human-made processes. It is broadly useful for creating models of random processes, making it a valuable tool in statistical analysis and research. Choice A is incorrect, as the normal distribution is commonly seen in many real-world phenomena. Choice B is also incorrect, as "normal" does not stand for "Non-linear Random Model, Axis Labelled." Choice C and E are both incorrect, as they include at least one incorrect statement.

Question 2

Which of the following is a useful summary of inferential statistics?
A)They help us decide whether our results are random.
B)They tell us whether our results are due to chance.
C)They help us decide between alternatives by comparing observed outcomes to models of random processes.
D)They help us decide between alternatives by comparing observed outcomes to central limits.
E)Both (c)and (d).

Accepted Answer

Inferential statistics are used to make inferences from data to more general conditions. They help us decide between alternatives by comparing observed outcomes to models of random processes, allowing us to determine if the observed effects are statistically significant or likely due to chance.

Question 3

Hamlet told Horatio that there were more things in heaven and earth than were dreamt of in his philosophy.In response, Horatio asked all philosophers with similar views to make a list of all the things they had dreamt of and asked them all to conduct a comprehensive count of all the things on earth.He planned to conduct a similar count of the things in heaven at a later stage but assumed that the distribution of things in heaven was similar to that for things on earth.Which of the following is true?
A)The test could not be statistically significant as Hamlet said "his" (i.e., Horatio's)philosophy so a double-blind design needed to be used for the other philosophers
B)A z-test may be appropriate for comparing the dreamed and observed counts on earth as the population standard deviation is known
C)A z-test may be appropriate for comparing the dreamed and observed counts in heaven as the population standard deviation is known.
D)A z-test may be appropriate for comparing the dreamed and observed counts in heaven as the population standard deviation is not known but it is assumed to be known
E)A z-test is inappropriate for comparing the dreamed and observed counts on earth as the population standard deviation is known but the variance is unknown.

Accepted Answer

C

Question 4

Acording to Tversky and Kahneman (1971), many researchers mistakenly believe that small samples are as representative of an underlying population as large samples.What do they refer to this as?
A)Belief in the law of large numbers.
B)Belief in the law of small numbers.
C)Belief in the law of large samples.
D)Belief in the law of small samples.
E)The inferential fallacy.

Accepted Answer

Tversky and Kahneman (1971) refer to this belief as the "law of small numbers," which is the mistaken assumption that small samples will behave like larger samples and be representative of the population. This can lead to inaccurate conclusions and generalizations.

Question 5

"A normal distribution with a mean of 0 and a standard deviation of 1.z-scores correspond to different points of the horizontal axis of the standard normal distribution, cutting off regions of different sizes." What is this a glossary definition of?
A)Standard distribution.
B)Cohen's normal distribution.
C)Standard normal distribution.
D)Normalized distribution.
E)z-standardization.

Accepted Answer

The term "standard normal distribution" refers specifically to a normal distribution with a mean of 0 and a standard deviation of 1. The use of z-scores to identify specific points on the distribution is a key characteristic of the standard normal distribution.

Question 6

"In an equation for a test statistic, the mathematical expression that estimates how much random error there is in the data".What is this a glossary definition of?
A)The random error term.
B)The error term.
C)The random term.
D)The unknown term.
E)The epistemological term.

Accepted Answer

The definition given refers to the error term, which represents the amount of random error in the data in an equation for a test statistic.

Question 7

"Statistical uncertainty arising from variation in observations around any measure of central tendency for which the researcher proposes no explanation.It is uncertainty in knowing or predicting individual scores on the basis of a measure of central tendency.This uncertainty is quantified by dispersion measures (e.g.standard deviation, variance, range)." What is this a glossary definition of?
A)Statistical uncertainty
B)Descriptive uncertainty
C)Inferential uncertainty
D)Dispersion uncertainty
E)Epistemological uncertainty

Accepted Answer

The answer of "Statistical uncertainty arising from variation in observations...

Question 8

"The distribution of the possible outcomes from a random process where there are two possible events (event p and event q)so that the probability of one or other occurring is 1 (and the probability of p occurring is 1 minus the probability of q occurring, i.e.p = 1 − q).An example would be the process of tossing an unbiased coin, where the probability of getting heads is .5 and the probability of getting tails is .5." What is this a glossary definition of?
A)The binomial distribution.
B)The pq distribution.
C)The paired quotient distribution.
D)The uniform distribution.
E)The probability distribution.

Accepted Answer

The description matches the binomial distribution, which models the number of successes in a fixed number of independent Bernoulli trials with a constant probability of success.

Question 9

A cognitive psychologist has developed a computer simulation of memory processes that generates a simulation of reaction times in response to the presentation of previously learned stimuli.The program has been designed to produce a mean reaction time of 200 msec with a standard deviation of 20.The psychologist is worried that the program has stopped working properly because the last 16 trials have produced a mean reaction time of 190 (with the expected standard deviation of 20).The researcher compares the two means using a z-test to ask whether the observed mean is lower than the expected mean.Which of the following statements is false?
A)A t-test could not be used on these data as the standard deviation is known.
B)A t-test could be used on these data even though the standard deviation is known but the z-test is the best option.
C)A t-test could be used on these data even though the standard deviation is known and it is a better option than the z-test because it can be done in SPSS.
D)A t-test could be used on these data but the z-test is the best option as it is simpler.
E)All of the above apart from (b).

Accepted Answer

A t-test is typically used when the population standard deviation is unknown and the sample size is small. However, even when the population standard deviation is known, a t-test can still be used, especially when the sample size is small (less than 30). The choice of a z-test in this scenario is appropriate due to the known population standard deviation, but stating that a t-test could not be used or is a worse option simply because the standard deviation is known or because of software capabilities is incorrect. The simplicity of the z-test makes it a good option, but it doesn't invalidate the use of a t-test.

Question 10

Which of the following statements is true?
A)Inferential statistics often involve comparing an information term to an error term.
B)Inferential statistics often involve dividing an information term by an error term.
C)Both (a)and (b).
D)Inferential statistics often involve dividing an error term by an information term.
E)Both (a)and (d).

Accepted Answer

Inferential statistics frequently involve dividing an information term by an error term to make inferences about a population from a sample. This is a common approach in hypothesis testing and constructing confidence intervals, where the goal is to determine if observed data significantly deviate from what is expected under a null hypothesis.

Question 11

The famous economist J M Keynes observed "In the long run we are all dead".Which of the following is demonstrated by this statement?
A)Keynes was a victim of the law of large numbers.
B)Keynes was a victim of the gambler's fallacy.
C)Keynes, being an economist and not a psychologist, did not understand the central limit theorem.
D)Keynes's statement is a prediction and we should ignore it unless it is testing a theory or it is associated with a significant p-value.
E)None of the above.

Accepted Answer

Keynes's statement is often interpreted to mean that economic policies should focus on addressing current problems rather than being overly concerned with potential long-term effects, as the long-term future is uncertain and unpredictable. It does not directly relate to the law of large numbers, gambler's fallacy, central limit theorem, or the significance of predictions in testing theories.

Question 12

If you had a room full of 100 people, which of the followng events is most unlikely.
A)Finding one person with an IQ over 120
B)Finding one person with an IQ over 140
C)Finding that the average IQ of people in the room was over 120
D)Finding that the average IQ of people in the room was over 140
E)It is impossible to answer this question without computing a z-score and refering to a table of areas under the normal curve.

Accepted Answer

It is more unlikely to find that the average IQ of people in the room is over 140 as it would require a higher proportion of individuals with exceptionally high IQs.

Question 13

You are asked to predict the outcome of a series of tosses of a fair coin.Which of the following is true?
A)To improve accuracy of prediction you are better off changing your guess from trial to trial as it is a random process.
B)To improve accuracy of prediction you are better off randomly selecting an alternative than trying to guess what will happen.
C)To improve accuracy of prediction you are better off sticking to the same alternative on each trial.
D)Extensive statistical training would help you improve your prediction of the coin toss by reducing the impact of the gambler's fallacy.
E)There is no way to improve accuracy of prediction for a fair coin toss.

Accepted Answer

Given that a fair coin toss is a completely random event with a 50/50 chance of landing on heads or tails, there is no strategy or pattern recognition that can improve the accuracy of predicting the outcome. Each toss is independent of the previous ones, making it impossible to increase prediction accuracy over pure chance.

Question 14

"A detailed statement about the likelihood of a particular set of events." What is this a glossary definition of?
A)A design statement.
B)A distribution model.
C)A probability map.
D)A statistical model.
E)A statistical survey.

Accepted Answer

A statistical model is a mathematical representation used to analyze and make predictions about real-world phenomena, where it often includes detailed statements about the likelihood of particular sets of events occurring.

Question 15

A cognitive psychologist has developed a computer simulation of memory processes that generates a simulation of reaction times in response to the presentation of previously learned stimuli.The program has been designed to produce a mean reaction time of 200 msec with a standard deviation of 20.The psychologist is worried that the program has stopped working properly because the last 16 trials have produced a mean reaction time of 190 (with the expected standard deviation of 20).Which of the following statements is true?
A)A z-score could be calculated for these data.
B)A z-score could be calculated for these data but no inferences could be made.
C)A z-score could be calculated for these data but no inferences could be made because it is impossible to get ethical clearance for computer simulations.
D)A z-score could be calculated but it could not be used to make inferences because the population standard deviation is unknown.
E)A z-score could be calculated but it could not be used to make inferences because the population standard deviation is likely to be a negative number.

Accepted Answer

A z-score can be calculated for these data by subtracting the sample mean reaction time (190) from the expected mean reaction time (200) and dividing by the standard deviation (20). However, it is important to note that this calculation assumes that the population standard deviation is known, which may not be the case. Further statistical analysis would be necessary to make inferences about the validity of the program. The statement about ethical clearance for computer simulations is irrelevant and incorrect.

Question 16

"The standard deviation of any sampling distribution.This is an estimate of random error in estimates of population parameters." What is this a glossary definition of?
A)Deviation error.
B)Random error.
C)Sampling error.
D)Population sampling error.
E)Estimated sampling eror.

Accepted Answer

The definition given describes sampling error, which is the difference between the sample statistic (such as mean or standard deviation) and the corresponding population parameter. The standard deviation of any sampling distribution is an estimate of how much random error is present in estimates of population parameters based on samples taken from the population.

Question 17

Which of the following statements is true?
A)The law of large numbers is another name for the gambler's fallacy.
B)In the long run the law of large numbers is another name for the gambler's fallacy.
C)The law of large numbers is the best way of avoiding standard errors.
D)The gambler's fallacy is an informal name for standard error.
E)None of the above.

Accepted Answer

None of the statements are true. The law of large numbers states that as the number of trials increases, the average outcome will converge to the expected value. The gambler's fallacy is the false belief that previous outcomes affect future outcomes in a random process. Standard error is a measure of the variability of sample means from the true population mean. None of these concepts are interchangeable or equivalent.

Question 18

"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?
A)Chance outcome.
B)Expected value.
C)Random event.
D)Random value.
E)Arbitrary outcomes in sampling space.

Accepted Answer

The definition given is that of expected value, which is the mean value of a probability distribution.

Question 19

Which of the following statement is true?
A)Standardization is a way of eliminating standard error
B)Randomization is a way of minimizing random error
C)Standardization is a way of eliminating random error
D)Randomization is a way of eliminating sampling error
E)Random sampling is a way of minimizing sampling error

Accepted Answer

Random sampling is a method used to minimize sampling error by ensuring that every member of the population has an equal chance of being included in the sample. This approach helps in creating a sample that is representative of the population, thereby reducing the bias and variability that can occur if the sample is not representative.

Question 20

"In an equation for a test statistic, the mathematical expression that estimates how much random error there is in the data." What is this a glossary definition of?
A)The test term.
B)The information term.
C)The random term.
D)The error term.
E)The full term.

Accepted Answer

The definition given is describing the error term in a test statistic equation.

Quiz 6: Some Principles of Statistical Inference

Which of the following is true of the normal distribution?

Which of the following is a useful summary of inferential statistics?

Acording to Tversky and Kahneman (1971) , many researchers mistakenly believe that small samples are as representative of an underlying population as large samples.What do they refer to this as?

"A normal distribution with a mean of 0 and a standard deviation of 1.z-scores correspond to different points of the horizontal axis of the standard normal distribution, cutting off regions of different sizes." What is this a glossary definition of?

"In an equation for a test statistic, the mathematical expression that estimates how much random error there is in the data".What is this a glossary definition of?

Which of the following statements is true?

The famous economist J M Keynes observed "In the long run we are all dead".Which of the following is demonstrated by this statement?

If you had a room full of 100 people, which of the followng events is most unlikely.

You are asked to predict the outcome of a series of tosses of a fair coin.Which of the following is true?

"A detailed statement about the likelihood of a particular set of events." What is this a glossary definition of?

"The standard deviation of any sampling distribution.This is an estimate of random error in estimates of population parameters." What is this a glossary definition of?

Which of the following statements is true?

"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?

Which of the following statement is true?

"In an equation for a test statistic, the mathematical expression that estimates how much random error there is in the data." What is this a glossary definition of?