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| Section | Objectives |
|---|---|
| Descriptive Statistics | - Data summarization
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| Probability Distributions | - Continuous distributions
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| Probability | - Fundamental probability concepts
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| Statistical Inference | - Estimation
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| Regression and Correlation | - Relationship analysis
|
>> Applied-Probability-and-Statistics인기자격증 시험대비 공부자료 <<
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질문 # 142
Confidence interval = sample mean ± ?
정답:A
설명:
A confidence interval for a population mean is generally constructed as sample mean ± margin of error. The margin of error equals a critical value multiplied by the standard error. Therefore, the structure is sample mean ± critical value × SE. The critical value depends on the confidence level and distribution used, such as a z critical value when the population standard deviation is known or a t critical value when it is unknown. The standard error measures the sampling variability of the sample mean, often computed as s/#n when using sample standard deviation. Option B is incorrect because variance times sample size is not a margin of error.
Option C is incomplete because standard deviation alone measures spread among data values, not uncertainty of the sample mean. Option D is incorrect because the median is a measure of center and is not the typical component of a mean-based confidence interval. Study Guide references/topics: confidence intervals, standard error, critical value, margin of error.
질문 # 143
Z-score negative #
정답:C
설명:
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.
질문 # 144
Probability of exactly 1 head in 2 coin flips = ?
정답:C
설명:
Two coin flips produce four equally likely ordered outcomes: HH, HT, TH, and TT. Exactly one head occurs in two of these outcomes: HT and TH. Therefore, the probability is 2 favorable outcomes out of 4 total outcomes, or 2/4 = 1/2. This can also be computed using the binomial model. There are n = 2 independent trials, success probability p = 1/2, and exactly one success is required. The binomial calculation is C(2,1)(1/2)