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| Section | Objectives |
|---|---|
| Topic 1: Probability Distributions | - Discrete distributions
|
| Topic 2: Descriptive Statistics | - Data summarization
|
| Topic 3: Regression and Correlation | - Relationship analysis
|
| Topic 4: Statistical Inference | - Hypothesis testing
|
| Topic 5: Probability | - Probability rules
|
>> Current WGU Applied-Probability-and-Statistics Exam Content <<
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NEW QUESTION # 127
A golf course is attempting to correlate golfing handicap with math SAT scores among local high school golfers. Ignoring potential confounding variables such as socioeconomic status, the golf course creates the following scatterplot.
What is the estimated value of r, the correlation coefficient, between these variables?
Answer: B
Explanation:
The correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables. In the scatterplot, the points are widely dispersed, so the relationship is weak rather than strong. The fitted trend line slopes slightly downward, indicating a negative association: as golf handicap increases, math SAT score tends to decrease slightly. Because the pattern is weak and negative, r should be close to 0 but less than 0. The best match is #0.10. Option A, #0.63, would represent a moderately strong negative linear relationship, which would require the points to cluster more tightly around a downward- sloping line. Option C, 0.10, has the right weak magnitude but the wrong direction because it is positive.
Option D, 0.63, is both too strong and positive. The visual evidence supports only a very slight negative linear association. References/topics from the Study Guide: scatterplots, correlation coefficient, positive and negative association, strength of linear relationship.
NEW QUESTION # 128
Correlation coefficient = #0.7. This indicates:
Answer: B
Explanation:
The correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables. Values of r range from #1 to 1. A negative value indicates that as one variable increases, the other variable tends to decrease. The value #0.7 is fairly close to #1, so it represents a strong negative linear relationship. It is not perfect, because perfect negative correlation would be r = #1, but it is clearly stronger than a weak association. Option B is incorrect because the sign is negative, not positive.
Option C is incorrect because no linear relationship would be represented by a correlation near 0. Option D is incorrect both in direction and strength. A scatterplot with r = #0.7 would generally show points trending downward from left to right, with some scatter around the trend. Study Guide references/topics: correlation coefficient, negative association, linear relationships, scatterplot interpretation.
NEW QUESTION # 129
R² = 0.81 # correlation r = ?
Answer: A
Explanation:
In simple linear regression, R² is the square of the correlation coefficient r. Therefore, to recover the possible correlation value from R², take the square root: r = ±#R². With R² = 0.81, the square root is #0.81 = 0.9, so r may be +0.9 or #0.9. The sign cannot be determined from R² alone because squaring removes direction. A positive r would indicate an upward linear association, while a negative r would indicate a downward linear association. Option D gives only +0.9, which would be correct only if the slope or scatterplot confirmed a positive relationship. Option B incorrectly treats R² as though it were r. Option C incorrectly keeps 0.81 after applying the square-root relationship. The technically complete answer is ±0.9. Study Guide references
/topics: coefficient of determination, correlation coefficient, regression, explained variation.
NEW QUESTION # 130
Best chart for categorical data?
Answer: A
Explanation:
A bar chart is the best display for categorical data because it shows the frequency or relative frequency of each category using separate bars. Categorical variables classify observations into groups, such as favorite color, type of transportation, political affiliation, or product category. A bar chart allows the viewer to compare category counts directly by bar height. A histogram is not appropriate because it is used for quantitative data grouped into numerical intervals. A scatterplot is used to examine the relationship between two quantitative variables, such as height and weight. A boxplot summarizes a quantitative distribution using quartiles, median, spread, and outliers. Since the question asks specifically about categorical data, the display must preserve category labels rather than numerical intervals or continuous measurement. Therefore, the bar chart is the correct choice. Study Guide references/topics: categorical data, bar charts, frequency displays, descriptive statistics.
NEW QUESTION # 131
Regression intercept represents:
Answer: C
Explanation:
In a linear regression equation, usually written as # = b# + b#x, the intercept b# represents the predicted value of Y when X equals 0. It is the point where the regression line crosses the vertical axis. For example, if a model is # = 12 + 3x, the intercept 12 means the predicted response is 12 when x = 0. The slope, b#, is different; it represents the predicted change in Y for each one-unit increase in X. Correlation measures the strength and direction of a linear association, not the intercept. The mean is a measure of center for a variable and is not the same as a regression intercept. In applied settings, the intercept is meaningful only when X = 0 is within a realistic or relevant range of the data. Study Guide references/topics: linear regression, intercept interpretation, slope-intercept form, response prediction.
NEW QUESTION # 132
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