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| Section | Objectives |
|---|---|
| Probability Theory | - Probability Distributions
|
| Descriptive Statistics | - Two Variable Data Analysis
|
| Statistical Inference | - Hypothesis Testing (Introductory Level)
|
| Regression and Modeling | - Linear Relationships
|
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NEW QUESTION # 43
Two independent events: P(A) = 0.3, P(B) = 0.2. P(A or B) = ?
Answer: D
Explanation:
For two events, the general addition rule is P(A or B) = P(A) + P(B) # P(A and B). Because A and B are independent, their joint probability is P(A and B) = P(A)P(B). Here, P(A) = 0.3 and P(B) = 0.2, so P(A and B)
= 0.3 × 0.2 = 0.06. Then P(A or B) = 0.3 + 0.2 # 0.06 = 0.44. The subtraction is necessary because the overlap, where both A and B occur, is counted twice when adding P(A) and P(B). Option A, 0.5, incorrectly adds the two probabilities without correcting for overlap. Option B gives the probability of both events, not either event. Option D is unrelated to the addition rule. Study Guide references/topics: independent events, addition rule, multiplication rule, union of events.
NEW QUESTION # 44
t-test used when:
Answer: D
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 # 45
Which measure of central tendency is least affected by outliers?
Answer: B
Explanation:
The median is the measure of central tendency least affected by outliers because it depends only on the ordered position of values, not on the numerical magnitude of extreme observations. To find the median, the data are arranged from least to greatest and the middle value is identified, or the average of the two middle values is taken when the sample size is even. If an extremely large or extremely small value is added to a data set, the mean can shift substantially because every value contributes to the arithmetic average. The median, however, usually remains stable unless the extreme value changes the middle position. The mode is also not directly affected by magnitude, but it may be absent or non-unique and is often less informative for numerical data. Range is not a measure of central tendency and is highly sensitive to outliers because it uses the minimum and maximum. Study Guide references/topics: descriptive statistics, measures of center, median, resistance to outliers.
NEW QUESTION # 46
Review the following inequality:
y # #4x + 1
Which shaded region is described by this inequality?
Answer: B
Explanation:
The inequality y # #4x + 1 has boundary line y = #4x + 1. The slope is #4, so the line must decrease steeply from left to right. The y-intercept is 1, so the line must cross the vertical axis at y = 1. Because the inequality uses "#," the boundary line must be solid, meaning points on the line are included in the solution set. The solution region must be below the line because y is less than or equal to the expression #4x + 1. A quick test point confirms this. Substitute (0, 0): 0 # #4(0) + 1, giving 0 # 1, which is true. Therefore, the shaded solution region must include the origin. Graph D shows a solid, steep downward-sloping line crossing the y-axis near 1 and shades the region containing the origin and below the boundary. References/topics from the Study Guide:
linear inequalities, slope-intercept form, boundary lines, test-point method.
NEW QUESTION # 47
Two dice rolled. Probability sum = 7?
Answer: A
Explanation:
When two standard six-sided dice are rolled, there are 6 × 6 = 36 equally likely ordered outcomes. To find the probability that the sum is 7, count all ordered pairs that produce 7. These are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are 6 favorable outcomes. Therefore, the probability is 6/36, which simplifies to 1/6. Since the answer choices include both 6/36 and 1/6, the listed answer from the PDF uses the unsimplified equivalent form, 6/36. Option C, 5/36, omits one valid ordered pair. Option D, 1/12, is too small because it would represent only 3 favorable outcomes out of 36. This problem reinforces that dice outcomes are ordered when two dice are rolled, so (1,6) and (6,1) are counted separately. Study Guide references/topics: sample spaces, dice probability, favorable outcomes, theoretical probability.
NEW QUESTION # 48
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