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| Section | Objectives |
|---|---|
| Statistical Inference | - Estimation and Confidence Intervals
|
| Regression and Modeling | - Linear Relationships
|
| Descriptive Statistics | - Single Variable Data Analysis
|
| Probability Theory | - Fundamental Probability Concepts
|
>> Applied-Probability-and-Statistics Examcollection <<
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NEW QUESTION # 107
Review the following inequality:
y < x # 1/2
Which shaded portion in the graphs corresponds to this inequality?
Answer: B
Explanation:
The inequality y < x # 1/2 has boundary line y = x # 1/2. This line has slope 1 and y-intercept #1/2, so it crosses the y-axis slightly below the origin and rises one unit for every one unit moved to the right. Because the inequality is strict, using " < " rather than "#," the boundary line must be dashed, showing that points on the line are not included in the solution set. The solution region must be shaded below the line because y is less than the expression x # 1/2. A useful verification method is the test point (0, 0). Substituting gives 0 < 0 #
1/2, or 0 < #1/2, which is false. Therefore, the region containing the origin should not be shaded. The fourth graph has the dashed boundary with intercept #1/2 and shades the region below the line while excluding the origin. References/topics from the Study Guide: graphing linear inequalities, slope-intercept form, dashed boundaries, test-point method.
NEW QUESTION # 108
Histogram is best for:
Answer: A
Explanation:
A histogram is used to display the frequency distribution of quantitative numerical data, especially continuous data grouped into intervals or bins. For example, a histogram can show the distribution of heights, test scores, commute times, or weights. Each bar represents a numerical interval, and the height of the bar represents how many observations fall within that interval. Unlike a bar chart, the bars in a histogram usually touch because the intervals form a continuous numerical scale. Option B is incorrect because categorical data are better displayed with a bar chart or pie chart. Option C is incorrect because a scatterplot displays the relationship between two quantitative variables, not the frequency distribution of one variable. Option D is incorrect because a boxplot summarizes median, quartiles, spread, and outliers rather than showing detailed frequency counts. The correct graph for continuous numerical frequency is a histogram. Study Guide references/topics:
histograms, quantitative data, frequency distributions, graphical displays.
NEW QUESTION # 109
Regression slope indicates:
Answer: D
Explanation:
In a linear regression equation, the slope represents the predicted change in the response variable Y for each one-unit increase in the explanatory variable X. In slope-intercept form, # = b# + b#x, the slope is b#. For example, if a regression equation predicts cost as # = 25 + 4x, the slope 4 means the predicted cost increases by 4 units for each additional unit of x. The intercept, b#, is the predicted value of Y when X = 0, so option B describes a different component. R² measures the proportion of variation in Y explained by the regression model, not the rate of change. Correlation measures strength and direction of linear association, but it is not the same as the slope because it is unitless and standardized. The slope is the operational rate of change in the model. Study Guide references/topics: linear regression, slope interpretation, response variable, explanatory variable.
NEW QUESTION # 110
Regression R² = 0.64. Interpretation?
Answer: D
Explanation:
The coefficient of determination, R², measures the proportion of variability in the response variable Y that is explained by the regression model using explanatory variable X. If R² = 0.64, then 64% of the variation in Y is explained by its linear relationship with X. The remaining 36% is unexplained by the model and may reflect other variables, random variation, measurement error, or nonlinear patterns. Option B is incorrect because R² is not the same as correlation. In simple linear regression, correlation r would be either +0.8 or #0.8, depending on the slope direction, because r² = 0.64. Option C is incorrect because the slope measures change in Y per one-unit change in X, not explained variation. Option D is incorrect because R² is not a probability of making a correct prediction. It is a proportion of variation accounted for by the model. Study Guide references
/topics: regression, coefficient of determination, explained variation, linear modeling.
NEW QUESTION # 111
A home inspector finds 3% of the homes in a community infected with termites.
How should the home inspector's findings be interpreted?
Answer: A
Explanation:
A probability or percentage describes how often an event is expected to occur in the long run. Here, 3% of homes are infected with termites. As a probability, this is 0.03, meaning about 3 out of every 100 homes would be expected to have termites. This is a small probability, so the event should be interpreted as unlikely.
It is not impossible, because impossible would require a probability of 0%. It is also not likely, because likely events generally have probabilities substantially greater than 50%. Finally, it is not "as likely as unlikely," because that language corresponds to a probability near 50%, where occurrence and nonoccurrence are approximately balanced. Since 3% is close to zero but not equal to zero, the technically correct interpretation is that termite infection is unlikely for a randomly selected home in the community. References/topics from the Study Guide: probability interpretation, percentages, unlikely events, complementary probability.
NEW QUESTION # 112
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