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| Section | Objectives |
|---|---|
| Statistical Inference | - Hypothesis testing
|
| Regression and Correlation | - Relationship analysis
|
| Descriptive Statistics | - Data summarization
|
| Probability Distributions | - Discrete distributions
|
| Probability | - Probability rules
|
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NEW QUESTION # 96
Variance of Poisson # = 5 = ?
Answer: C
Explanation:
A defining property of the Poisson distribution is that its variance equals its mean, and both are equal to #.
Since the question states # = 5, the variance is also 5. This property distinguishes the Poisson distribution from many other probability distributions. The mean represents the expected number of events per interval, while the variance describes the spread of the event count around that mean. In a Poisson model with # = 5, event counts tend to vary around 5, and the numerical variance is 5. Option B, 4, option C, 0, and option D, 1, do not follow from the Poisson variance rule. The result is not obtained by squaring # or taking its square root; it is simply equal to #. Study Guide references/topics: Poisson distribution, variance, mean, # parameter.
NEW QUESTION # 97
A sample of 100 houses was surveyed in each of two states: Georgia and Kansas. Square footages of the houses are summarized by state in the following side-by-side box plots.
What is the interquartile range for house sizes in Georgia?
Answer: D
Explanation:
The interquartile range, or IQR, measures the spread of the middle 50% of a distribution. It is calculated as Q3
# Q1, where Q1 is the first quartile and Q3 is the third quartile. In the Georgia box plot, the left edge of the box is labeled 800, representing Q1, and the right edge of the box is labeled 2800, representing Q3. Therefore, the interquartile range is 2800 # 800 = 2000 square feet. The minimum value, 500, and maximum value, 5000, are part of the full range, not the IQR. The median, 1200, identifies the center of the distribution but is not used directly in the IQR calculation. Option D, 4500, corresponds to the full range from 500 to 5000, not the interquartile range. The correct interpretation is that the middle half of Georgia house sizes spans 2000 square feet. References/topics from the Study Guide: box plots, quartiles, interquartile range, comparing distributions.
NEW QUESTION # 98
Expected value = ?
Answer: B
Explanation:
Expected value is the theoretical long-term average outcome of a random variable over many repeated trials.
It is calculated by multiplying each possible value by its probability and then summing those products. For a discrete random variable, E(X) = #xP(x). Expected value does not necessarily have to be an outcome that can occur in one trial. For example, the expected value of rolling a fair six-sided die is 3.5, even though no face shows 3.5. It represents the balance point of the probability distribution. The median is the middle value of an ordered distribution, and the mode is the most likely or most frequent value. Expected value may equal 0 in some distributions, but it is not defined as 0. The best conceptual definition is long-term average. Study Guide references/topics: expected value, random variables, probability distributions, long-run average.
NEW QUESTION # 99
Confidence interval = sample mean ± ?
Answer: C
Explanation:
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.
NEW QUESTION # 100
Probability of rolling an odd number on a die:
Answer: A
Explanation:
A standard six-sided die has six equally likely outcomes: 1, 2, 3, 4, 5, and 6. The odd outcomes are 1, 3, and
5. Thus, there are 3 favorable outcomes out of 6 possible outcomes. The probability is 3/6, which simplifies to
1/2. This means an odd number is just as likely as an even number on a fair die. Option B, 1/3, would represent 2 favorable outcomes out of 6, which is not correct. Option C, 1/6, is the probability of rolling one specific number, such as only a 1. Option D, 2/3, would require 4 favorable outcomes out of 6. Since exactly half the faces are odd, the probability is one-half. Study Guide references/topics: theoretical probability, equally likely outcomes, sample space, favorable outcomes.
NEW QUESTION # 101
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