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| Section | Objectives |
|---|---|
| Descriptive Statistics | - Two Variable Data Analysis
|
| Statistical Inference | - Hypothesis Testing (Introductory Level)
|
| Probability Theory | - Fundamental Probability Concepts
|
| Regression and Modeling | - Linear Relationships
|
>> Applied-Probability-and-Statistics Exam Actual Questions <<
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NEW QUESTION # 95
In hypothesis testing, rejecting H# when true = ?
Answer: D
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 # 96
Determine x:
4 + x = 6 # x
Answer: A
Explanation:
The equation 4 + x = 6 # x is a linear equation in one variable. To solve it, collect variable terms on one side and constant terms on the other. Add x to both sides to eliminate the negative x on the right: 4 + 2x = 6. Then subtract 4 from both sides: 2x = 2. Finally, divide both sides by 2, giving x = 1. This value can be verified directly in the original equation. Substituting x = 1 gives 4 + 1 = 5 on the left and 6 # 1 = 5 on the right, so both sides are equal. Option A gives 4 = 6, which is false. Option C gives 6 = 4, also false. Option D gives 9 =
1, which is not valid. The correct solution is the value that balances both sides of the equation. References
/topics from the Study Guide: basic algebra, solving linear equations, inverse operations, substitution checks.
NEW QUESTION # 97
Two dice rolled, probability of both even = ?
Answer: D
Explanation:
A standard six-sided die has three even outcomes: 2, 4, and 6. Thus, the probability that one die lands on an even number is 3/6 = 1/2. When two dice are rolled, the outcomes are independent because the result of one die does not affect the other. Therefore, the probability that both dice are even is 1/2 × 1/2 = 1/4.
Equivalently, there are 36 ordered outcomes for two dice. The even-even outcomes are formed from 3 even choices on the first die and 3 even choices on the second die, giving 3 × 3 = 9 favorable outcomes. Then 9/36 simplifies to 1/4. Option B gives the probability of one die being even, not both. Options C and D do not match the count or multiplication rule. Study Guide references/topics: independent events, dice probability, multiplication rule, sample space.
NEW QUESTION # 98
Mean = 50, SD = 5, n = 25. Standard error = ?
Answer: C
Explanation:
The standard error of the mean measures the expected sampling variability of the sample mean. It is calculated by dividing the sample standard deviation by the square root of the sample size: SE = s / #n. In this question, the standard deviation is 5 and the sample size is 25. Therefore, SE = 5 / #25 = 5 / 5 = 1. The mean of 50 identifies the center of the sample distribution but is not directly used in the standard error calculation.
Option B, 5, is the standard deviation, not the standard error. Option C, 25, is the sample size. Option D, 0.2, would result from incorrectly dividing 5 by 25 rather than by the square root of 25. The distinction between standard deviation and standard error is important: standard deviation describes spread among individual observations, while standard error describes spread among sample means. Study Guide references/topics:
standard error, standard deviation, sample size, sampling distributions.
NEW QUESTION # 99
95% confidence interval for mean = (45, 55). Which statement is correct?
Answer: D
Explanation:
A 95% confidence interval provides a plausible range of values for an unknown population mean based on sample data. The interval (45, 55) means the method used to construct the interval captures the true population mean in approximately 95% of repeated samples under the same conditions. In practical exam language, the correct interpretation is that the population mean is estimated to lie within the interval with 95% confidence. Option B states the midpoint of the interval, 50, but the question asks for the correct confidence interval interpretation, not just the center. Option C is incorrect because the population mean is not always the upper endpoint. Option D is imprecise because once an interval is computed, it is fixed; the confidence level refers to the long-run success rate of the procedure, not a changing probability attached to that exact fixed interval. Study Guide references/topics: confidence intervals, population mean, point estimate, margin of error.
NEW QUESTION # 100
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