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| Section | Objectives |
|---|---|
| Regression and Correlation | - Relationship analysis
|
| Descriptive Statistics | - Data visualization
|
| Probability Distributions | - Discrete distributions
|
| Probability | - Fundamental probability concepts
|
| Statistical Inference | - Hypothesis testing
|
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NEW QUESTION # 75
What is the mode of this dataset: 3, 5, 7, 7, 10?
Answer: A
Explanation:
The mode is the value that occurs most frequently in a data set. In the set 3, 5, 7, 7, 10, the value 3 appears once, 5 appears once, 10 appears once, and 7 appears twice. Since 7 has the highest frequency, it is the mode.
This question tests recognition of a measure of center that differs from the mean and median. The mean would require summing all values and dividing by the number of observations, while the median would identify the middle value after ordering the data. The data are already ordered, and the middle value is also 7, but the reason the correct answer is 7 here is specifically because it appears more often than any other value. Options A, B, and D each name values that occur only once, so none can be the mode. A dataset may have one mode, multiple modes, or no mode, but this dataset is unimodal. References/topics from the Study Guide: descriptive statistics, measures of center, frequency, mode.
NEW QUESTION # 76
In hypothesis testing, rejecting H# when true = ?
Answer: A
Explanation:
A Type I error occurs when the null hypothesis, H#, is true but the test decision rejects it. In plain statistical language, this is a false positive: the analysis concludes that there is evidence of an effect, difference, or relationship when in reality the null condition is true. The probability of making a Type I error is denoted by
#, the significance level, commonly set at 0.05. A Type II error is different; it occurs when the null hypothesis is false but the test fails to reject it. That is a false negative. Option C is incorrect because rejecting a true null is not a correct decision. Option D describes not rejecting or accepting the null, not the stated event. The critical phrase is "rejecting H# when true," which directly defines a Type I error. Study Guide references
/topics: hypothesis testing, null hypothesis, Type I error, significance level.
NEW QUESTION # 77
Conditional probability formula:
Answer: B
Explanation:
Conditional probability measures the probability that event A occurs given that event B has already occurred.
The formula is P(A|B) = P(A and B)/P(B), assuming P(B) is greater than zero. The denominator P(B) restricts the sample space to cases where B occurs, and the numerator P(A and B) counts cases where both A and B occur within that restricted space. Option B is incorrect because it divides P(A) by P(B) without requiring overlap between A and B. Option C reverses the conditioning and would relate to P(B|A) only if the numerator were P(A and B). Option D applies to independent events when finding P(A and B), not to conditional probability in general. The vertical bar in P(A|B) is read as "given," and it signals that the denominator should be the probability of the given event. Study Guide references/topics: conditional probability, joint probability, event intersection, probability rules.
NEW QUESTION # 78
Correlation coefficient r = #0.5 #
Answer: B
Explanation:
The correlation coefficient r describes the direction and strength of a linear relationship between two quantitative variables. Its values range from #1 to +1. A negative value indicates that as one variable increases, the other tends to decrease. Since r = #0.5, the direction is negative. Its magnitude, 0.5, is not close enough to zero to indicate no relationship, but it is also not close enough to #1 to represent an extremely strong relationship. Therefore, the best description is a moderate negative linear relationship. Option B is incorrect because the sign is negative, not positive. Option C is incorrect for both direction and strength.
Option D would be appropriate only when r is near 0, indicating little or no linear association. A scatterplot with r = #0.5 would generally show a downward trend, but with noticeable scatter around the trend. Study Guide references/topics: correlation coefficient, negative association, scatterplots, linear relationship strength.
NEW QUESTION # 79
Probability of rolling an even number on a six-sided die?
Answer: C
Explanation:
A standard six-sided die has six equally likely outcomes: 1, 2, 3, 4, 5, and 6. The even outcomes are 2, 4, and
6. That gives 3 favorable outcomes out of 6 total outcomes. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2. Option A, 1/3, would correspond to 2 favorable outcomes out of 6, which is not correct here. Option C, 1/6, is the probability of rolling one specific number, such as only a 2.
Option D, 2/3, would require 4 favorable outcomes out of 6. Since exactly half of the die faces are even and half are odd, the probability of rolling an even number is one-half. Study Guide references/topics: theoretical probability, equally likely outcomes, sample space, favorable outcomes.
NEW QUESTION # 80
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