Question 1

If a set of standardized test scores is normally distributed,having a mean of 75 and a standard deviation of 6,approximately 95 percent of the scores are somewhere between

Accepted Answer

In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. Here, two standard deviations from the mean (75) is 75 ± 2(6) = 75 ± 12, which gives us a range from 63 to 87.

Question 2

Gene believes he is much more likely to win the state lottery if he chooses the numbers than if the numbers are randomly generated by a computer program.Gene's belief best illustrates

Accepted Answer

Gene's belief that he can increase his chances of winning the lottery by choosing the numbers himself reflects an illusion of control, which is the tendency to believe that we have more control over outcomes than we actually do. In reality, the odds of winning the lottery are determined solely by chance, and the method by which the numbers are chosen (by a computer program or by an individual) has no effect on the outcome.

Question 3

Approximately what percentage of the cases represented by the normal curve fall between -2 and +2 standard deviations from the mean?

Accepted Answer

Approximately 95% of the cases in a normal distribution fall within 2 standard deviations from the mean, according to the empirical rule.

Question 4

Which of the following correlations expresses the strongest degree of relationship between two variables?

Accepted Answer

The correlation coefficient ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation between two variables. 
Therefore, a correlation coefficient of -0.67 has the strongest degree of negative relationship between two variables.

Question 5

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 between 55 and 145?

Accepted Answer

The answer of If IQ scores are normally distributed,having a...

Question 6

A positive correlation indicates

Accepted Answer

A positive correlation indicates that as one variable increases, the other variable also increases. This demonstrates a direct relationship between the two variables.

Question 7

Professor Alonzo is conducting a research study to determine the relationship between test performance and amount of time spent studying among college students.A variable in this study is

Accepted Answer

The variable in this study is the amount of time spent studying, as it is being investigated for its relationship with test performance. The other options (Professor Alonzo, college students, and participants) are not variables in this particular study, but rather the context or individuals involved.

Question 8

Which of the following correlations between annual income and education level would best enable you to predict annual income on the basis of level of education?

Accepted Answer

A correlation coefficient of +0.50 indicates a moderate positive correlation between annual income and education level. This means that as education level increases, annual income is likely to increase as well. Therefore, this correlation would be the best choice for predicting annual income based on level of education. Choices A, B, and C have correlation coefficients that are too weak to reliably predict annual income based on education level.

Question 9

The perception of a relationship between two variables that does not exist is called a(n)

Accepted Answer

An illusory correlation refers to the perception of a relationship between two variables that does not exist. This can occur due to cognitive biases or other factors that lead us to incorrectly believe that two variables are related when they are not truly correlated.

Question 10

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

Accepted Answer

A pattern that extends from lower left to upper right on a scatterplot suggests a positive correlation between the two variables depicted. Positive correlation means that as one variable increases, the other variable also tends to increase.

Question 11

Approximately 68 percent of the cases represented by the normal curve fall within ________ standard deviation(s)of the mean.

Accepted Answer

Approximately 68 percent of the data within a normal distribution falls within one standard deviation of the mean. This is a fundamental property of the normal distribution, also known as the empirical rule or 68-95-99.7 rule.

Question 12

Kiska displayed the relationship between college students' self-esteem and their feelings of depression on a scatterplot.The points on the scatterplot are most likely clustered in a pattern that

Accepted Answer

A scatterplot showing the relationship between college students' self-esteem and their feelings of depression would likely show a negative correlation, where higher levels of self-esteem are associated with lower levels of depression, resulting in points that extend from the upper left (high depression, low self-esteem) to the lower right (low depression, high self-esteem).

Question 13

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 between 85 and 115?

Accepted Answer

The percentage of people who have IQ scores between 85 and 115 can be found by using the empirical rule for a normal distribution. According to this rule, approximately 68% of the data falls within one standard deviation from the mean. Since the mean IQ score is 100 and the standard deviation is 15, one standard deviation below the mean is 85 (100-15) and one standard deviation above the mean is 115 (100+15). Therefore, approximately 68% of people have IQ scores between 85 and 115.

Question 14

Which of the following statistical measures is most helpful for indicating the extent to which people's happiness predicts the number of friends they have?

Accepted Answer

The correlation coefficient measures the strength and direction of the relationship between two variables, in this case, happiness and number of friends. A positive correlation coefficient would indicate that as happiness increases, the number of friends increases as well. Therefore, the correlation coefficient is the most helpful statistical measure to indicate the extent to which people's happiness predicts the number of friends they have.

Question 15

A negative correlation indicates

Accepted Answer

A negative correlation means that as one variable increases, the other variable decreases. This is also known as an inverse relationship. Option A describes a positive correlation, while options C and D describe measures of variability that are not related to correlation.

Question 16

A correlation coefficient is a statistical measure of the

Accepted Answer

A correlation coefficient measures the extent to which two factors vary together, indicating the strength and direction of the relationship between two variables. A correlation coefficient can range from -1 to +1, with a score of 0 indicating no correlation.

Question 17

On average,Caryl's school bus arrives on time,although sometimes it is a bit early or late.If the arrival times are distributed on a normal curve,which of the following statistics would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day?

Accepted Answer

The standard deviation in a normal distribution measures the dispersion or variability around the mean, indicating how spread out the values are. Knowing the standard deviation allows one to estimate the probability of a value (in this case, the bus's arrival time) falling within a certain range around the mean (the scheduled arrival time).

Question 18

A scatterplot graphically depicts the

Accepted Answer

A scatterplot is a visual representation of the relationship between two variables. It plots one variable on the x-axis and the other variable on the y-axis, and each data point is represented by a dot. The pattern or shape of the dots can give an indication of the strength and direction of the relationship between the two variables. Therefore, a scatterplot is best used to depict the degree of relationship between two variables.

Question 19

Professor Chang displays the relationship between the height and weight measurements of over 500 randomly selected people on a scatterplot.The points on the scatterplot are most likely clustered in a pattern that

Accepted Answer

The pattern of the scatterplot between height and weight is generally positive, meaning as height increases, weight tends to increase as well. Thus, the points are likely clustered in a pattern that extends from the lower left to the upper right of the plot.

Question 20

Professor Caste wants to examine the relationship between watching television and substance use.Which type of statistic would be best for this type of research study?

Accepted Answer

A correlation would be the best choice to examine the relationship between watching television and substance use. Correlation measures the strength and direction of the relationship between two variables, in this case, the amount of television watched and substance use. Inferential statistics and score distributions are not relevant in this context. Descriptive statistics could be used to summarize the frequency of watching television and substance use, but they would not provide information about the relationship between the two variables.

Quiz 16: Statistical Reasoning in Everyday Life