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| Section | Objectives |
|---|---|
| Regression and Correlation | - Relationship analysis
|
| Statistical Inference | - Estimation
|
| Descriptive Statistics | - Data summarization
|
| Probability | - Fundamental probability concepts
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| Probability Distributions | - Discrete distributions
|
>> Accurate Applied-Probability-and-Statistics Answers <<
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NEW QUESTION # 149
Type II error occurs when:
Answer: C
Explanation:
A Type II error occurs when the null hypothesis is false but the statistical test fails to reject it. In many answer choices, this is expressed as "accepting the null when false," though the more precise language is "failing to reject the null." This error is a false negative: the test misses a real effect, difference, or relationship. For example, if a medication truly improves recovery but a study fails to detect sufficient evidence of improvement, that is a Type II error. Option B describes a Type I error, which occurs when a true null hypothesis is rejected. Option C is not an error. Option D is too vague; statistical decision errors refer specifically to incorrect conclusions about hypotheses, not ordinary data-entry mistakes. The probability of a Type II error is denoted #, and statistical power is 1 # #. Study Guide references/topics: hypothesis testing, Type II error, null hypothesis, statistical power.
NEW QUESTION # 150
Standard error decreases when:
Answer: A
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 # 151
A teacher plots the test scores of a class using the box plot.
What is true about the test scores?
Answer: B
Explanation:
A box plot displays the five-number summary of a quantitative data set: minimum, first quartile, median, third quartile, and maximum. The median is represented by the vertical line inside the box. In the given box plot, that internal vertical line is positioned at 80 on the score axis. Therefore, the median test score for Class A is
80 points. The value 70 corresponds to the left edge of the box, which represents the first quartile, not the median. The value near 88 represents the right edge of the box, which is the third quartile. The whiskers extend to the approximate minimum and maximum scores, but those values do not determine the median. The median divides the ordered data into two equal halves, meaning about 50% of the students scored at or below
80 and about 50% scored at or above 80. References/topics from the Study Guide: box plots, five-number summary, median, quartiles.
NEW QUESTION # 152
Binomial expected value = ?
Answer: B
Explanation:
For a binomial random variable, the expected value is E(X) = np, where n is the number of trials and p is the probability of success on each trial. The binomial model applies when there is a fixed number of independent trials, each trial has two outcomes, and the probability of success remains constant. The expected value represents the long-run average number of successes across repeated binomial experiments. For example, if a test has 20 independent questions and the probability of success on each is 0.75, the expected number correct is 20 × 0.75 = 15. Option B, n/p, and option C, p/n, do not represent the binomial mean. Option D, n + p, incorrectly adds the number of trials and success probability, which are not comparable units. The formula np captures both how many opportunities there are and how likely success is on each opportunity. Study Guide references/topics: binomial distribution, expected value, success probability, discrete random variables.
NEW QUESTION # 153
Dataset: 3, 5, 7, 9, 11. Median = ?
Answer: B
Explanation:
The median is the center value of an ordered dataset. The values 3, 5, 7, 9, and 11 are already arranged from least to greatest. Because there are five observations, the median is the third value, with two observations below it and two observations above it. The third value is 7, so the median is 7. The median is a measure of central tendency that describes the middle position of the data rather than the arithmetic average. In this dataset, the mean is also 7 because the values are evenly spaced around 7, but the median is determined by position, not by summing and dividing. Option B is the second value, option C is the fourth value, and option D is not a data value. The correct answer is the value that splits the ordered list into two equal halves. Study Guide references/topics: median, ordered data, measures of center, descriptive statistics.
NEW QUESTION # 154
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