Statistics MCQs
Topic Notes: Statistics
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
1
If the sample mean is 40, what population parameter is this value typically used to estimate?
Answer:
U
In statistical notation, the sample mean is commonly used as a point estimator for the population mean, often denoted by the Greek letter mu (μ), which is represented here as 'U'. This estimator is unbiased, meaning its expected value is equal to the population mean.
2
How many primary types of statistical estimation are commonly recognized in inferential statistics?
Answer:
Two
In statistical inference, estimation is broadly categorized into two main types: point estimation and interval estimation. Point estimation involves providing a single numerical value as an estimate of a population parameter, while interval estimation provides a range of values (a confidence interval) within which the parameter is expected to lie with a certain level of confidence.
3
What term describes the difference between the true population parameter and its corresponding point estimate?
Answer:
error of estimation
The error of estimation, often referred to as the sampling error, represents the discrepancy between a population parameter and the statistic used to estimate it. This difference arises because the sample is only a subset of the population, and it is a fundamental concept in inferential statistics used to determine the precision of an estimate.
4
Determine the confidence interval if the point estimate is 8 and the margin of error is 5.
Answer:
3 to 13
A confidence interval is calculated by taking the point estimate and adding/subtracting the margin of error. Lower bound = 8 - 5 = 3. Upper bound = 8 + 5 = 13. Thus, the interval is 3 to 13.
5
What is the general mathematical structure used to calculate a confidence interval for a population parameter?
Answer:
point estimate ± margin of error
A confidence interval is constructed by taking a point estimate (such as the sample mean) and adding and subtracting a margin of error to create a range that likely contains the true population parameter.
6
In the context of regression estimation, the sample ratio serves as an unbiased estimator for which population parameter?
Answer:
ratio
In survey sampling, the ratio estimator is used to estimate the population ratio of two variables. While it is generally a biased estimator for the population ratio in small samples, it is often used as the standard estimator for the population ratio parameter.
7
Estimation is formally classified as a component of which branch of statistics?
Answer:
Statistical Inference
Statistical inference is the process of drawing conclusions about a population based on sample data. Estimation, which involves using sample statistics to estimate population parameters (point or interval estimation), is a fundamental pillar of this branch.
8
If a population parameter is 10 and its point estimate is 15, what is the calculated error of estimation?
Answer:
5
The error of estimation is defined as the absolute difference between the estimated value and the true population parameter. In this case, the calculation is |15 - 10| = 5. This represents the magnitude of the deviation of the estimate from the actual parameter value.
9
Which of the following terms can be used to describe a statistic?
Answer:
Both A and B
A statistic is a function of sample data. When viewed as a random variable used to estimate a population parameter, it is called an estimator. Once the sample data is collected and the function is evaluated, the resulting numerical value is called an estimate.
10
In the context of confidence interval estimation, what is another term often used to describe the interval estimate?
Answer:
confidence efficient
While 'confidence interval' is the standard terminology, some older or specific statistical texts refer to the resulting range as a confidence coefficient or interval estimate. The term 'confidence efficient' appears to be a specific nomenclature used in the source material provided, though it is not standard in modern statistical literature.