Commerce MCQs
Topic Notes: Commerce
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
Due to the additive nature of the chi-square distribution, how can multiple chi-square values derived from similar data samples be combined?
Answer:
adding
The chi-square distribution possesses an additive property, meaning that if independent chi-square variables are summed, the resulting sum also follows a chi-square distribution with degrees of freedom equal to the sum of the individual degrees of freedom.
2
When a numerical measure describes a population, it is called a parameter; what is the corresponding term for a measure derived from a sample?
Answer:
Statistic
In statistical inference, a parameter is a fixed value representing a characteristic of the entire population. A statistic is a numerical value calculated from sample data, which is used as an estimator to make inferences about the unknown population parameter.
3
Evaluate the following statements: Statement I: Rejecting a true null hypothesis is defined as a Type II error. Statement II: When the sample size is small and the population standard deviation is unknown, the Z-test is the most appropriate statistical test.
Answer:
Both statements are false
Statement I is false because rejecting a true null hypothesis is a Type I error, not Type II. Statement II is false because when the sample size is small and the population standard deviation is unknown, the t-test is the appropriate choice, not the Z-test, which requires a known population standard deviation or a large sample size.
4
In a Chi-square test, if the expected frequency in a cell is less than 5, what is the standard procedure regarding adjacent cells?
Answer:
5
To ensure the validity of the Chi-square test, expected frequencies should generally be at least 5. If a cell has an expected frequency below 5, it is common practice to combine it with an adjacent cell to reach a total of 5 or more.
5
The Z-test is mathematically and conceptually most closely related to which of the following statistical tests?
Answer:
T-test
The Z-test and the t-test are both used to test hypotheses about population means. The primary difference is that the Z-test is used when the population standard deviation is known or the sample size is large, whereas the t-test is used when the population standard deviation is unknown and the sample size is small. They share the same underlying logic of comparing observed means to expected values.
6
Evaluate the assertion and reason regarding the chi-square test: (A) Expected values should be at least 5. (R) The chi-square distribution provides an adequate approximation of the sampling distribution.
Answer:
Both (A) and (R) are true, and (R) is the right explanation
The chi-square test relies on the assumption that the sampling distribution of the test statistic approximates the chi-square distribution. This approximation is only valid when the expected frequencies in each cell are sufficiently large, typically at least 5, to ensure the validity of the test results.
7
Which of the following statements regarding statistical terminology is accurate?
Answer:
All of the above
A statistic is a numerical measure calculated from a sample, whereas a parameter is a measure derived from an entire population (census). A census is defined as the process of surveying every member of a population.
8
Evaluate the following statements regarding hypothesis testing: Statement I: An alternative hypothesis of μ ≠ μ0 necessitates a two-tailed test. Statement II: The mean of the sampling distribution of the mean is not equal to the population mean.
Answer:
Statement I is true, while Statement II is false
Statement I is true because a non-directional hypothesis (μ ≠ μ0) requires testing in both tails of the distribution. Statement II is false because, according to the Central Limit Theorem, the mean of the sampling distribution of the sample mean is equal to the population mean (μ).
9
Given a large population where the ratio of the standard error of the mean (SEx) to the population standard deviation (σ) is 8:40, what is the sample size (n)?
Answer:
25
The standard error of the mean is calculated as SEx = σ / sqrt(n). Given SEx/σ = 8/40 = 1/5, it follows that 1/sqrt(n) = 1/5. Squaring both sides gives 1/n = 1/25, therefore n = 25. This calculation is standard in statistical sampling theory for determining sample size requirements.
10
The sampling distribution of the mean represents the distribution of which of the following?
Answer:
sample statistics
The sampling distribution of the mean is the probability distribution of the sample means obtained from all possible samples of a specific size drawn from a population. It is a distribution of sample statistics.