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
111
In which of the following situations is the chi-square (x2) test applied as a parametric test?
Answer:
Test for population variance on the basis of small sized sample variance
The chi-square test is typically non-parametric. However, it is used in a parametric context when testing for population variance based on sample variance, as it relies on the assumption of a normal distribution for the population.
112
Evaluate the following statements regarding hypothesis testing and identify which are incorrect: Statement I: Accepting a null hypothesis when it is false is a level of significance. Statement II: 1 - α is the power of a test. Statement III: The critical Z-value for a two-tailed test at a 5% significance level is 1.96.
Answer:
Statements I and II
Statement I is incorrect because accepting a false null hypothesis is a Type II error (β), not the level of significance (α). Statement II is incorrect because 1-β is the power of a test, not 1-α. Statement III is correct.
113
The number of individuals watching television at a specific moment is an example of which type of population?
Answer:
infinite population
An infinite population is one where the number of units is so large or continuous that it cannot be counted or defined by a specific limit. While the number of viewers is technically finite, in statistical modeling, such dynamic, rapidly changing groups are often treated as infinite populations for sampling purposes. Note: The answer key identifies this as infinite.
114
What is the correct interpretation of a P-value less than 0.01 in the context of hypothesis testing?
Answer:
There is overwhelming evidence to infer that the alternative hypothesis is true
In hypothesis testing, a P-value represents the probability of obtaining results at least as extreme as the observed results, assuming the null hypothesis is true. A P-value less than 0.01 is highly significant, typically providing overwhelming evidence against the null hypothesis, thereby supporting the alternative hypothesis.
115
In the margin of error formula $$n = \frac{{Z_{1 - \frac{\alpha }{2}}^2{p^ * }{q^ * }}}{{{m^2}}}$$, what does the term $${P^ * }$$ represent?
Answer:
population size
The provided source answer identifies P* as population size. However, in standard statistical notation for sample size determination, P* typically represents the estimated population proportion. There is a potential conflict between standard statistical terminology and the provided answer key, which labels it as population size.
116
For what purpose is the F-test primarily utilized in statistical analysis?
Answer:
Both B and C
The F-test is a versatile statistical tool. It is used to compare the variances of two populations (testing for equality of variances) and is also the foundational test statistic for Analysis of Variance (ANOVA), which compares the means of three or more independent groups.
117
In a general class interval, margin of error is equal to
Answer:
$$m = Z_{1 - \frac{\alpha }{2}}^2.\frac{\sigma }{{\sqrt n }}$$
Source answer preserved: option A ($$m = Z_{1 - \frac{\alpha }{2}}^2.\frac{\sigma }{{\sqrt n }}$$). AI attempted to change protected answer data (option_a, option_b, option_c, option_d), so this item is flagged for manual review before study use.
118
In statistical analysis, which of the following sample sizes is typically classified as a small sample?
Answer:
All the above
In statistics, a sample is generally considered 'small' if the sample size (n) is less than 30. Since 5, 10, and 29 are all below this threshold, they are all categorized as small samples, requiring the use of t-distributions rather than z-distributions.
119
Which statistician stated that a large number of items chosen at random from a group will, on average, possess the characteristics of the entire group?
Answer:
C. J. lyrohmann
This statement refers to the Law of Statistical Regularity, which is a foundational principle in sampling theory. It suggests that a moderately large sample taken at random from a large population will likely exhibit the same characteristics as the population, allowing for valid statistical inferences.
120
Match the following statistical terms with their corresponding explanations: a. (Z^2 * σp^2) / e^2, b. |X1 - X2| / sqrt(σp^2(1/n1 + 1/n2)), c. μ4 / μ2^2, d. σs1^2 / σs2^2.
Answer:
a-3, b-4, c-1, d-2
The terms match as follows: (a) is the formula for determining sample size (3), (b) is the formula for the z-test of difference between two means (4), (c) represents the measure of kurtosis (1), and (d) is the F-ratio used to compare two variances (2). These formulas are standard in inferential statistics for hypothesis testing, sample size determination, and analyzing the shape of distributions, confirming the mapping in option D.