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| Section | Objectives |
|---|---|
| Topic 1: Probability Theory | - Fundamental Probability Concepts
|
| Topic 2: Regression and Modeling | - Linear Relationships
|
| Topic 3: Statistical Inference | - Estimation and Confidence Intervals
|
| Topic 4: Descriptive Statistics | - Single Variable Data Analysis
|
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NEW QUESTION # 101
One-sample t-test compares:
Answer: B
Explanation:
A one-sample t-test is used to compare a sample mean to a hypothesized or known population mean when the population standard deviation is unknown and the data are approximately normal or the sample size is sufficiently large. The test statistic evaluates how far the sample mean is from the hypothesized mean in standard error units. Option A is therefore correct. A two-sample t-test compares means from two independent groups, so option B describes a different test. Tests of variances use procedures such as chi-square or F-based methods depending on context, so option C is not appropriate. Tests of proportions use z procedures for categorical success/failure data, not a one-sample t-test for means. The t-test is part of inferential statistics because it uses sample evidence to make a decision about a population parameter. Study Guide references
/topics: one-sample t-test, sample mean, population mean, hypothesis testing.
NEW QUESTION # 102
A single ball is drawn from an opaque bag that contains red, blue, and green balls. The probability of drawing a red ball is .3, and the probability of drawing a blue ball is .6.
What is the probability of drawing a green ball?
Answer: B
Explanation:
The probabilities of all possible outcomes in a sample space must sum to 1. In this experiment, the bag contains only red, blue, and green balls, so these three outcomes exhaust the sample space. The probability of drawing a red ball is 0.3, and the probability of drawing a blue ball is 0.6. Their combined probability is 0.3 +
0.6 = 0.9. The remaining probability must belong to drawing a green ball. Therefore, P(green) = 1 # 0.9 = 0.1.
This can also be viewed as a complement problem: green is the complement of drawing either red or blue when those are the only other colors available. Option B repeats the red probability, option C would make the total probability exceed 1, and option D is the combined probability of red or blue rather than green.
References/topics from the Study Guide: probability sum rule, complements, sample space, mutually exclusive outcomes.
NEW QUESTION # 103
Two mutually exclusive events: P(A and B) = ?
Answer: D
Explanation:
Mutually exclusive events cannot occur at the same time. If event A occurs, event B cannot occur, and if event B occurs, event A cannot occur. Therefore, the probability of both events occurring together is zero: P (A and B) = 0. For example, when rolling one die, the event "roll a 2" and the event "roll a 5" are mutually exclusive because one roll cannot produce both outcomes simultaneously. Option B applies to independent events, not mutually exclusive events. In fact, mutually exclusive events with positive probabilities are not independent because the occurrence of one eliminates the possibility of the other. Option C is part of the addition rule for mutually exclusive events when calculating P(A or B), not P(A and B). Option D would mean both events always occur together, which contradicts mutual exclusivity. Study Guide references/topics:
mutually exclusive events, joint probability, addition rule, probability foundations.
NEW QUESTION # 104
Standard error decreases when:
Answer: C
Explanation:
The standard error of the mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Because n appears in the denominator under a square root, increasing the sample size decreases the standard error when the standard deviation is held constant. This reflects a central idea in sampling: larger samples tend to produce more stable and precise estimates of the population mean. Option C is incorrect because increasing the standard deviation increases the standard error, not decreases it. Option B is incomplete and does not identify what is decreasing. Option D is not the direct driver of standard error; confidence level affects the critical value and margin of error, but the standard error itself is determined by variability and sample size. The correct relationship is inverse: as sample size increases, standard error decreases. Study Guide references/topics: standard error, sample size, sampling variability, precision of estimates.
NEW QUESTION # 105
Correlation coefficient r = #0.5 #
Answer: B
Explanation:
The correlation coefficient r describes the direction and strength of a linear relationship between two quantitative variables. Its values range from #1 to +1. A negative value indicates that as one variable increases, the other tends to decrease. Since r = #0.5, the direction is negative. Its magnitude, 0.5, is not close enough to zero to indicate no relationship, but it is also not close enough to #1 to represent an extremely strong relationship. Therefore, the best description is a moderate negative linear relationship. Option B is incorrect because the sign is negative, not positive. Option C is incorrect for both direction and strength.
Option D would be appropriate only when r is near 0, indicating little or no linear association. A scatterplot with r = #0.5 would generally show a downward trend, but with noticeable scatter around the trend. Study Guide references/topics: correlation coefficient, negative association, scatterplots, linear relationship strength.
NEW QUESTION # 106
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