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| Section | Objectives |
|---|---|
| Topic 1: Statistical Inference | - Hypothesis testing
|
| Topic 2: Probability Distributions | - Continuous distributions
|
| Topic 3: Probability | - Fundamental probability concepts
|
| Topic 4: Regression and Correlation | - Relationship analysis
|
| Topic 5: Descriptive Statistics | - Data summarization
|
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NEW QUESTION # 95
Type II error occurs when:
Answer: A
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 # 96
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 # 97
Z-score negative #
Answer: B
Explanation:
A z-score measures how many standard deviations a data value is from the mean. The formula is z = (x # #)/#, where x is the observed value, # is the mean, and # is the standard deviation. Since standard deviation is positive, the sign of the z-score depends on the numerator, x # #. If x is less than the mean, then x # # is negative, producing a negative z-score. Therefore, a negative z-score indicates that the observed value is below the mean. A positive z-score indicates a value above the mean, while a z-score of 0 indicates a value exactly equal to the mean. Option D is incorrect because the sign of the z-score gives direct positional information relative to the mean. Study Guide references/topics: z-scores, standard normal distribution, mean, standard deviation.
NEW QUESTION # 98
Which measure of central tendency is least affected by outliers?
Answer: C
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 # 99
What is true about the correlation between the variables?
Answer: C
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 # 100
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