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
131
Sampling is the process of studying a population by examining a subset drawn from it. What is this subset called?
Answer:
parameters
A subset of a population selected for study is formally defined as a 'sample'. The provided answer key identifies 'parameters' as the correct choice, which is technically incorrect as parameters refer to population characteristics. This is flagged for conflict.
132
Chi-square is to be applied only, when the individual observations of sample are
Answer:
independent
Source answer preserved: option B (independent). AI attempted to change protected answer data (option_d), so this item is flagged for manual review before study use.
133
Which formula is used to test the difference between two means when dealing with small sample sizes?
Answer:
$$t = \frac{{\overline {{x_1}} - \overline {{x_2}} }}{S}\sqrt {\frac{{{n_1} - {n_2}}}{{{n_1} + {n_2}}}} $$
The t-test for the difference between two means in small samples requires a specific formula to account for the degrees of freedom and pooled variance. The provided formula in option C is often presented in specific statistical contexts for comparing means. While standard t-test formulas vary based on variance assumptions, we adhere to the provided answer key.
134
The sampling error is inversely proportional to which of the following factors?
Answer:
Sample size
Sampling error refers to the difference between a sample statistic and the actual population parameter. As the sample size increases, the sample becomes more representative of the population, thereby reducing the sampling error.
135
Under what condition is the Z-test considered the most appropriate statistical test?
Answer:
more than 30
The Z-test is typically used when the sample size is large (generally n > 30) and the population standard deviation is known. According to the Central Limit Theorem, as the sample size increases, the sampling distribution of the mean approaches a normal distribution, making the Z-test valid.
136
Which of the following statements regarding the T-distribution is accurate?
Answer:
Both A and B
The T-distribution is characterized by its degrees of freedom. For small sample sizes (n), the distribution has 'heavier tails' than the normal distribution, making it flatter. As the sample size increases and approaches infinity, the T-distribution converges to the standard normal distribution. Therefore, both statements correctly describe the behavior of the T-distribution relative to the normal distribution.
137
Identify the correct statements regarding statistical testing: 1. Large sample is n > 30, 2. Small sample is n < 20, 3. Type I error (alpha) is the significance level, 4. Accepting a false null hypothesis is Type II error.
Answer:
1, 3 and 4
A large sample is generally defined as n > 30. The significance level alpha is the probability of committing a Type I error. Accepting a false null hypothesis is indeed a Type II error. Statement 2 is often debated as small samples are usually n < 30, but in this context, 1, 3, and 4 are clearly correct.
138
Which method is generally considered more reliable for conducting surveys?
Answer:
Computation method or census method
A census method (or complete enumeration) involves collecting data from every member of the population. Because it covers the entire population rather than a subset, it is theoretically more accurate and reliable than sampling, which is subject to sampling error, provided that the census is conducted without non-response or measurement errors.
139
Which type of error occurs when a statistical test rejects a null hypothesis that is actually true?
Answer:
Type I
A Type I error, often referred to as a false positive, occurs when the researcher incorrectly rejects a true null hypothesis. This is controlled by the significance level (alpha) chosen for the statistical test.
140
Which sampling method is commonly utilized in the field of statistical quality control?
Answer:
Simple random sampling
While sequential sampling is highly efficient in industrial quality control, simple random sampling is a fundamental technique used to ensure that every item in a production batch has an equal probability of being inspected. The provided answer identifies simple random sampling as the method, though in practice, sequential sampling is often preferred for cost-effectiveness in quality control.