Question 1

Colette received an unusually high grade of A on her first biology test and a B+ on the second,even though she studied equally for both tests. Which of the following best explains Colette's deteriorating pattern of performance?

Accepted Answer

Regression toward the mean suggests that extreme scores on a test are likely to be followed by less extreme scores on a subsequent test. Colette's high grade on her first test was likely due to chance and thus her subsequent lower grade is a regression toward her true mean performance.

Question 2

Which of the following correlation coefficients expresses the weakest degree of relationship between two variables?

Accepted Answer

The correlation coefficient of -0.12 indicates a weak and negative relationship between the two variables. The closer the correlation coefficient is to 0, the weaker the relationship between the two variables. Therefore, A is the best choice as it has the lowest absolute value among the given options.

Question 3

If the points on a scatterplot are clustered in a pattern that extends from the upper left to the lower right,this would suggest that the two variables depicted are

Accepted Answer

When points on a scatterplot extend from the upper left to the lower right, it indicates that as one variable increases, the other decreases, which is the definition of a negative correlation.

Question 4

Statistical reasoning can help us to generalize correctly from

Accepted Answer

Statistical reasoning helps us to make inferences about the larger population based on a smaller sample. By using statistical methods, we can estimate population parameters with a certain level of confidence and generalize the findings from the sample to the population. The other answer choices are not accurate applications of statistical reasoning.

Question 5

If a positive correlation between two sets of scores is displayed as a scatterplot,the points are clustered in a pattern that

Accepted Answer

A positive correlation means that as one variable increases, the other variable tends to increase as well. This is represented in a scatterplot by points that cluster in a pattern that extends from the lower left to the upper right of the graph. Therefore, the best choice is B, as it describes the appropriate pattern for a positive correlation.

Question 6

A normal curve would approximate the distribution of

Accepted Answer

The physical heights of all American women would likely follow a normal distribution, as there would be a range of heights with most women falling around a central average height and fewer women at the extremes of very tall or very short heights. The other options do not necessarily have a clear and predictable bell-shaped curve of distribution.

Question 7

The illusion that uncontrollable events are correlated with our actions is facilitated by a statistical phenomenon known as

Accepted Answer

Regression toward the mean is when extreme or unusual scores on a variable tend to be followed by less extreme scores. This can create the illusion of a correlation between our actions and uncontrollable events because we tend to only notice when an extreme event is immediately followed by our action, and not when it is not.

Question 8

Approximately what percentage of the cases represented by the normal curve fall between -3 and +3 standard deviations from the mean?

Accepted Answer

Approximately 99.7% of the data falls within 3 standard deviations from the mean in a normal distribution, which is closest to 100%.

Question 9

Approximately what percentage of the cases represented by the normal curve fall between -1 and +1 standard deviations from the mean?

Accepted Answer

According to the empirical rule or 68-95-99.7 rule, approximately 68% of the cases represented by the normal curve fall between -1 and +1 standard deviations from the mean.

Question 10

If IQ scores are normally distributed,having a mean of 100 and a standard deviation of 15,approximately what percentage of people have IQ scores somewhere between 70 and 130?

Accepted Answer

In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. Since 70 and 130 are two standard deviations below and above the mean of 100, respectively, about 95% of people have IQ scores in this range.

Question 11

To represent graphically the correlation between two variables,researchers often construct a

Accepted Answer

Scatterplot is the best choice to represent the correlation between two variables graphically. It shows the relationship between two variables by plotting individual data points on a two-dimensional graph with one variable on each axis, allowing the visual identification of trends or patterns in the data.

Question 12

The precision with which a sample average approximates a population average increases as

Accepted Answer

The precision with which a sample average approximates a population average increases as the standard deviation of the sample decreases. This is because a smaller standard deviation indicates that the values in the sample are closer together and therefore more representative of the population as a whole.

Question 13

Gamblers often throw dice gently for low numbers and hard for high numbers. This most directly illustrates

Accepted Answer

The behavior of throwing the dice gently for low numbers and hard for high numbers is an example of an illusion of control, where individuals believe they can influence the outcome of a random event through their actions. This belief is often seen in gamblers who have superstitions or rituals that they believe will increase their chances of winning.

Question 14

Professor Connolly uses a scatterplot to display the relationship between students' intelligence test scores and the number of failing grades they have received. The points on the plot are most likely clustered in a pattern that

Accepted Answer

It is likely that students with higher intelligence test scores will have fewer failing grades, and vice versa, resulting in a diagonal line that extends from the lower left to the upper right of the plot. This is commonly known as a negative correlation.

Question 15

After sports magazines give cover-story attention to the outstanding performance of an athlete,the individual often suffers a real decline in performance. This may be at least partially explained in terms of

Accepted Answer

Regression toward the mean refers to the statistical phenomenon where extreme values tend to move closer to the average over time. So, if an athlete had an outstanding performance, it may have been due to some degree of luck or chance, and their subsequent performances will likely regress towards their average level of performance. This can lead to a decline in performance, which may be mistakenly attributed to the attention from the sports magazine.

Question 16

Which of the following statistical measures is most helpful for indicating the extent to which IQ scores can be used to predict grades in school?

Accepted Answer

The correlation coefficient is a statistical measure that indicates the strength and direction of the linear relationship between two variables. In this case, we can use it to determine the extent to which IQ scores and grades in school are related. A strong positive correlation would suggest that higher IQ scores are associated with higher grades, while a weak or negative correlation would suggest that IQ scores are not a good predictor of school grades. The mean, standard deviation, and range are measures of central tendency and variability, but they do not provide information about the relationship between two variables.

Question 17

Approximately 95 percent of the cases represented by the normal curve fall within ________ standard deviation(s)from the mean.

Accepted Answer

The empirical rule states that approximately 68% of cases fall within 1 standard deviation from the mean, 95% fall within 2 standard deviations from the mean, and 99.7% fall within 3 standard deviations from the mean. Therefore, the best choice is B, as 95 percent of cases fall within 2 standard deviations from the mean.

Question 18

If a set of standardized test scores is normally distributed,having a mean of 50 and a standard deviation of 10,approximately 68 percent of the group members receive scores somewhere between

Accepted Answer

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Since the mean is 50 and the standard deviation is 10, one standard deviation above and below the mean would be 40 and 60, respectively.

Question 19

Which of the following is a statistical measure of both the direction and the strength of a relationship between two variables?

Accepted Answer

The correlation coefficient measures the strength and direction of a linear relationship between two variables. The other options (B-D) are measures of variability or central tendency but do not address the relationship between two variables.

Question 20

Which of the following correlations between self-esteem and body weight would enable you to most accurately predict body weight from knowledge of level of self-esteem?

Accepted Answer

A correlation coefficient of +0.60 indicates a relatively strong positive relationship between self-esteem and body weight. This means that as self-esteem increases, body weight tends to increase as well. Therefore, based on knowledge of an individual's level of self-esteem, we could more accurately predict their body weight when there is a strong positive relationship between these variables.

Quiz 3: Self-Concept: Who Am I