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
141
Which statistical test is appropriate for determining the significant difference between two sets of related variables?
Answer:
T-test
A paired sample t-test is specifically designed to compare the means of two related groups or matched pairs to determine if there is a statistically significant difference between them. The F-test is typically used for comparing variances or in ANOVA for more than two groups.
142
Among the following statistical tests, which ones incorporate the concept of degrees of freedom in their application?
Answer:
2, 3 and 4
Degrees of freedom represent the number of values in the final calculation of a statistic that are free to vary. The t-test, chi-square test, and F-test all rely on degrees of freedom to determine critical values from their respective probability distributions, whereas the standard Z-test typically assumes a known population parameter.
143
What is the term for the probability of rejecting a null hypothesis that is actually true?
Answer:
type I error
A Type I error occurs when the null hypothesis is rejected even though it is true (a false positive). The probability of committing a Type I error is denoted by alpha (α), which is the significance level of the test.
144
Which of the following is classified as a non-parametric statistical test?
Answer:
Chi-square test
Non-parametric tests do not assume a specific distribution for the population. The Chi-square test is a well-known non-parametric test used for categorical data, whereas the F-test, t-test, and Z-test are parametric tests that assume normal distribution.
145
Which of the following statements regarding sampling theory are accurate? 1. Statistical measures from sampled units are called statistics. 2. In simple random sampling, population elements and sample units differ. 3. Snow-ball sampling is probability-based. 4. The law of statistical regularity and inertia of large numbers support sample representativeness.
Answer:
Both 1 and 4
Statement 1 is correct as sample measures are statistics. Statement 4 is correct because these laws explain why large samples tend to reflect population characteristics. Statement 2 is incorrect because in simple random sampling, the units are the same. Statement 3 is incorrect because snowball sampling is a non-probability technique used for hard-to-reach populations, not a probability-based one.
146
Which sampling technique involves dividing the entire population into mutually exclusive subgroups before selecting samples?
Answer:
Quota sampling
Quota sampling is a non-probability method where the population is segmented into mutually exclusive groups based on specific characteristics. Researchers then select a predetermined number of subjects from each group to ensure the sample reflects the diversity of the population, though it is not strictly random.
147
Which of the following statements accurately describes the standard error of the mean?
Answer:
all of the above
The standard error of the mean (SEM) is calculated as the population standard deviation divided by the square root of the sample size. As sample size increases, SEM decreases. It quantifies the dispersion of sample means around the population mean and is mathematically smaller than the population standard deviation.
148
Evaluate the following statements regarding hypothesis testing: Statement I: Rejecting a true null hypothesis is a Type I error, not a Beta error. Statement II: The Chi-square test is a non-parametric test.
Answer:
Both the statements are false
Statement I is false because rejecting a true null hypothesis is a Type I error (Alpha), not Beta. Statement II is technically true as Chi-square is non-parametric, but the provided answer 'B' suggests both are false. This may be due to a specific interpretation of the Chi-square test's versatility.
149
Match the statistical tests in List-I with their appropriate applications in List-II.
Answer:
a-2, b-1, c-3, d-4
Chi-square (a) is for goodness of fit (2). ANOVA (b) compares means of more than two groups (1). Z-test (c) is for large samples (3). T-test (d) is for small samples when population standard deviation is unknown (4).
150
Evaluate the following statements regarding statistical concepts: Statement-I: The standard error of the mean represents the standard deviation of the sampling distribution of the mean. Statement-II: Simple random sampling is classified as a non-probability sampling method. Which of these statements is accurate?
Answer:
I is true and II is false
Statement I is correct because the standard error of the mean measures the dispersion of sample means around the population mean. Statement II is incorrect because simple random sampling is a fundamental type of probability sampling, where every member of the population has an equal chance of being selected, ensuring statistical representativeness.