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| Section | Objectives |
|---|---|
| Descriptive Statistics | - Two Variable Data Analysis
|
| Regression and Modeling | - Linear Relationships
|
| Statistical Inference | - Estimation and Confidence Intervals
|
| Probability Theory | - Probability Distributions
|
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NEW QUESTION # 88
Two events mutually exclusive # P(A and B) = ?
Answer: B
Explanation:
Mutually exclusive events cannot happen at the same time. Therefore, the probability of their intersection is zero: P(A and B) = 0. For instance, on a single coin toss, the event "heads" and the event "tails" are mutually exclusive because a single toss cannot produce both outcomes. Option B applies to independent events when calculating the probability of both occurring, but mutually exclusive events with positive probabilities are not independent because one event prevents the other from occurring. Option C is used to find P(A or B) for mutually exclusive events, not P(A and B). Option D would mean both events always occur together, which directly contradicts mutual exclusivity. The word "and" is the key operator: it asks for overlap. Since mutually exclusive events have no overlap, the result is 0. Study Guide references/topics: mutually exclusive events, intersections, joint probability, addition rule.
NEW QUESTION # 89
Standard error decreases when:
Answer: D
Explanation:
The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Since n appears in the denominator, increasing the sample size reduces the standard error, assuming the standard deviation stays constant. This reflects the fact that larger samples produce more stable estimates of the population mean. Option B is incorrect because decreasing sample size increases standard error. Option C is incorrect because a larger standard deviation increases standard error by increasing the numerator. Option D is incorrect because the mean affects the center of the distribution but does not directly determine the standard error. Standard error is about precision: smaller standard error means less sampling variability and a more precise estimate. That is why larger samples are preferred in inference. Study Guide references/topics: standard error, sample size, standard deviation, sampling variability.
NEW QUESTION # 90
What is true about the correlation between the variables?
Answer: A
Explanation:
The scatterplot shows a clear downward pattern: as x increases, y tends to decrease. This establishes a negative correlation. The strength of a correlation is judged by how closely the points follow a general linear pattern. Here, although the points are not perfectly aligned, they form a visible descending band from upper left to lower right. That pattern is much stronger than a weak association, where the points would appear widely scattered with only a slight trend. Therefore, the best description is a strong negative correlation.
Options C and D are incorrect because they describe positive correlation, which would require y to increase as x increases. Option A correctly identifies the negative direction but understates the strength of the pattern. In correlation terminology, a strong negative value would have r substantially below 0 and closer to #1 than to 0.
References/topics from the Study Guide: scatterplots, negative correlation, correlation strength, bivariate quantitative data.
NEW QUESTION # 91
A gardener records the length of a plant over a duration of 35 weeks. The scatterplot shows the data.
What is the relationship between length and time?
Answer: A
Explanation:
The scatterplot shows time on the horizontal axis and plant length on the vertical axis. As time increases, the plotted plant lengths also increase. This upward pattern indicates a positive relationship. The points are not randomly scattered; they follow a clear rising trend from approximately 3 inches at the beginning to more than 9 inches near the end of the observation period. Because the points cluster closely around an increasing pattern, the relationship is strong rather than weak. A negative relationship would require plant length to decrease as time increases, which is not shown. A weak positive relationship would show only a slight upward tendency with substantial scatter, but this graph shows a consistent increase across the weeks.
Therefore, the best description is a strong positive relationship between time and plant height or length.
References/topics from the Study Guide: scatterplots, association, positive correlation, strength of relationship.
NEW QUESTION # 92
Standard deviation squared = ?
Answer: C
Explanation:
Variance and standard deviation are directly connected measures of spread. Variance is calculated by averaging squared deviations from the mean, while standard deviation is the square root of variance.
Therefore, reversing that relationship, standard deviation squared equals variance. Symbolically, if the standard deviation is s, then the sample variance is s². This relationship matters because variance is expressed in squared units, while standard deviation is expressed in the original units of measurement. For example, if test-score standard deviation is 4 points, the variance is 4² = 16 square points. The mean and median are measures of center, not squared spread. The standard error measures the variability of a sample statistic, usually the sample mean, across repeated samples. The correct answer is variance because it is the squared form of standard deviation. Study Guide references/topics: standard deviation, variance, measures of spread, descriptive statistics.
NEW QUESTION # 93
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