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| Section | Objectives |
|---|---|
| Regression and Correlation | - Relationship analysis
|
| Probability | - Probability rules
|
| Statistical Inference | - Estimation
|
| Probability Distributions | - Discrete distributions
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| Descriptive Statistics | - Data summarization
|
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NEW QUESTION # 112
Which graph displays data in a manner that is accurate?
Answer: B
Explanation:
The accurate display is the bar graph labeled "Number of Feet Traveled" with the vertical axis showing the number of feet and the horizontal axis identifying the student travelers. For discrete observations associated with individual students, a bar graph is appropriate because each bar represents a separate category or individual and its height represents the measured value. Option A is inaccurate because its title states
"Number of Miles Traveled," while the vertical axis is labeled in feet; this creates a unit mismatch. Option C uses a pie chart, which is designed to show parts of a whole, not individual measured distances unless the goal is proportional composition. Option D uses a line graph, which is typically reserved for ordered change, especially over time; connecting student traveler values implies continuity or trend that is not justified. The correct graph must use consistent units, clear labels, and an appropriate display type. References/topics from the Study Guide: data displays, bar graphs, categorical identifiers, quantitative measurements, graph accuracy.
NEW QUESTION # 113
Sample correlation r = 0.6. R² = ?
Answer: A
Explanation:
The coefficient of determination, R², is obtained by squaring the correlation coefficient r in simple linear regression. Here, r = 0.6, so R² = (0.6)² = 0.36. This means that 36% of the variability in the response variable is explained by the linear relationship with the explanatory variable. The remaining 64% of variability is not explained by that linear model and may be due to other variables, random variation, measurement error, or nonlinear structure. Option B gives the correlation itself, not its square. Option C would come from squaring
0.4, not 0.6. Option D would imply a perfect explanatory relationship, which would require |r| = 1. The value of R² is always between 0 and 1 and is commonly interpreted as a proportion of explained variation. Study Guide references/topics: correlation, coefficient of determination, regression, explained variation.
NEW QUESTION # 114
Regression slope indicates:
Answer: C
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 # 115
t-test used when:
Answer: B
Explanation:
A t-test is used when making inferences about a population mean and the population standard deviation, #, is unknown. In practical settings, # is rarely available, so the sample standard deviation, s, is used as an estimate.
That substitution introduces additional uncertainty, which is why the t-distribution is used instead of the standard normal distribution. The t-distribution has heavier tails, especially for small samples, reflecting the extra variability caused by estimating # from the sample. Option B describes a z-test setting, where the population standard deviation is known. Option C is incorrect because categorical population data are usually analyzed with proportions, chi-square tests, or related categorical procedures, not mean-based t-tests. Option D is invalid because t-tests have a clear inferential role. The controlling condition is unknown #, with inference focused on means. Study Guide references/topics: t-tests, unknown population standard deviation, sample standard deviation, inferential statistics.
NEW QUESTION # 116
Sum of probabilities in sample space = ?
Answer: C
Explanation:
The probabilities of all outcomes in a complete sample space must sum to 1. A sample space contains every possible outcome of a probability experiment, and one of those outcomes must occur. For example, when rolling a fair six-sided die, the outcomes are 1, 2, 3, 4, 5, and 6. Each has probability 1/6, and the sum is 1/6 +
1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1. A total probability of 0 would mean no outcome can occur, which is impossible for a valid experiment. A total greater than 1 violates probability rules because probabilities cannot exceed certainty. "Cannot exceed 2" is too broad and mathematically invalid, since the exact total must equal
1. This principle is foundational for checking probability distributions and validating whether assigned probabilities are coherent. Study Guide references/topics: sample space, probability axioms, total probability, theoretical probability.
NEW QUESTION # 117
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