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| Section | Objectives |
|---|---|
| Probability Theory | - Probability Distributions
|
| Descriptive Statistics | - Single Variable Data Analysis
|
| Statistical Inference | - Hypothesis Testing (Introductory Level)
|
| Regression and Modeling | - Linear Relationships
|
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NEW QUESTION # 104
Chi-square test used for:
Answer: D
Explanation:
A chi-square test is commonly used to analyze categorical data, especially to determine whether two categorical variables are associated. In a chi-square test of independence, data are arranged in a contingency table, and observed cell counts are compared with expected cell counts under the assumption that the variables are independent. If the observed counts differ substantially from the expected counts, there is evidence of association between the categorical variables. For example, a chi-square test could examine whether voting preference is associated with age group or whether product preference differs by region.
Option B describes comparing means, which is typically handled by a t-test or related procedure. Option C refers to regression, which models relationships between variables, often involving quantitative outcomes.
Option D refers to variance, which is tested using different procedures depending on context. The key phrase is "categorical variables": chi-square methods work with counts in categories. Study Guide references/topics:
categorical data, contingency tables, chi-square test, association.
NEW QUESTION # 105
Binomial distribution parameters = ?
Answer: D
Explanation:
A binomial distribution is defined by two parameters: n and p. The parameter n is the fixed number of trials, and p is the probability of success on each trial. The model applies when trials are independent, each trial has two possible outcomes, and p remains constant. For example, if X is the number of heads in 10 fair coin flips, then X follows a binomial distribution with n = 10 and p = 0.5. Option B, #, is the parameter of a Poisson distribution, used for counts of events over intervals. Option C, # and #, commonly describes a normal distribution, where # is the mean and # is the standard deviation. Option D is incorrect because the binomial model has a precise parameter structure. Identifying n and p is essential before calculating binomial probabilities or expected value. Study Guide references/topics: binomial distribution, independent trials, success probability, discrete probability.
NEW QUESTION # 106
Conditional probability P(A|B) = P(A and B)/P(B) #
Answer: C
Explanation:
The formula for conditional probability is P(A|B) = P(A and B)/P(B), provided P(B) > 0. The notation P(A|B) is read as "the probability of A given B." The denominator P(B) restricts the sample space to cases in which B occurs, and the numerator P(A and B) counts the portion of that restricted group in which A also occurs.
Therefore, the statement is true. Option B is incorrect because the formula is the standard definition of conditional probability. Option C is incorrect because if A and B are mutually exclusive, then P(A and B) = 0, which creates a special case rather than the general definition. Option D is invalid because conditional probability is undefined when P(B) = 0. The condition must have positive probability. Study Guide references
/topics: conditional probability, joint probability, event intersection, probability rules.
NEW QUESTION # 107
Variance formula = ?
Answer: D
Explanation:
The sample variance formula is s² = #(x# # x#)² / (n # 1). In this formula, x# represents each data value, x# is the sample mean, and n is the sample size. The expression x# # x# gives each value's deviation from the mean. Squaring the deviations prevents negative and positive deviations from canceling and emphasizes larger departures. Dividing by n # 1 gives the sample variance, using degrees of freedom to correct bias when estimating population variance from a sample. Option B is the formula for the sample mean, not variance.
Option C squares the mean and does not measure spread. Option D resembles part of the standard deviation process but omits division by n # 1 and is not the variance formula. Variance is foundational because standard deviation is the square root of variance. Study Guide references/topics: variance, sample variance formula, mean deviations, measures of spread.
NEW QUESTION # 108
Poisson distribution mean = ?
Answer: B
Explanation:
For a Poisson distribution, the mean is #, pronounced "lambda." The parameter # represents the expected number of events occurring in a fixed interval, such as calls per hour, defects per batch, or arrivals per minute.
A defining feature of the Poisson distribution is that both the mean and variance are equal to #. Therefore, if X follows a Poisson distribution with # = 4, then the expected value, or mean, is 4, and the variance is also 4.
Option B and option C are only correct in special cases where # happens to equal 0 or 1, not generally. Option D is conceptually related because the Poisson variance equals #, but the question asks for the mean, and the parameter name is #. The Poisson distribution is used for discrete counts of events over a fixed interval under a constant average rate. Study Guide references/topics: Poisson distribution, expected value, variance, # parameter.
NEW QUESTION # 109
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