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
121
What term describes the degree of confidence with which we assert that a specific population parameter falls within a defined range?
Answer:
level of confidence
The level of confidence (or confidence level) represents the probability that a confidence interval will contain the true population parameter. It quantifies the reliability of the estimation process. For example, a 95% confidence level means that if we were to take many samples, 95% of the calculated intervals would contain the actual population parameter.
122
What are the degrees of freedom for a chi-square test conducted on a contingency table with 3 rows and 4 columns?
Answer:
6
The degrees of freedom for a chi-square test of independence in a contingency table is calculated using the formula (r - 1) * (c - 1), where r is the number of rows and c is the number of columns. Given 3 rows and 4 columns, the calculation is (3 - 1) * (4 - 1) = 2 * 3 = 6.
123
How is sampling error characterized in the context of incomplete enumeration?
Answer:
existent
Sampling error refers to the difference between a sample statistic and the actual population parameter. Because sampling involves observing only a portion of the population rather than the entire group, this error is inherently existent in any study based on incomplete enumeration.
124
When a researcher selects respondents for a poll using a telephone directory, which sampling method is being employed?
Answer:
convenience sampling
Using a telephone directory is a form of convenience sampling because the researcher selects participants based on their easy accessibility and availability in the directory. While it is a common method, it often introduces bias because it excludes individuals without phones or those not listed, meaning it does not provide a truly random representation of the entire population.
125
A machine produced 20 defective items out of 400. After maintenance, it produced 10% defectives in a batch of 300. Which hypothesis test is suitable to determine if the machine's performance has improved?
Answer:
Test of significance of difference between two sample proportion (one tail test)
To compare the defect rates before and after maintenance, we must compare two independent sample proportions. Since the objective is to determine if there is an improvement (a directional change), a one-tailed test for the difference between two proportions is the correct statistical method to apply.
126
Which statement accurately describes the behavior of a parameter versus a statistic when drawing repeated random samples from a population?
Answer:
Values of a statistic will vary according to the sampling distribution for that statistic
A parameter is a fixed numerical characteristic of a population, whereas a statistic is a variable calculated from sample data. Because samples differ, the resulting statistics vary, forming a sampling distribution. The statistic's variation is described by its specific sampling distribution, while the parameter remains constant for the population.
127
Which statistical test is most appropriate for evaluating the effectiveness of a special coaching program on student marks?
Answer:
Paired f test
A paired t-test (often referred to as a paired sample t-test) is used to compare the means of two related groups, such as the same students' marks before and after receiving special coaching, to determine if there is a statistically significant difference.
128
What is the primary purpose of conducting a post-hoc test following an ANOVA analysis?
Answer:
Describe those groups that have reliable differences between group means
ANOVA determines if there is a statistically significant difference among three or more group means. However, it does not specify which specific groups differ. Post-hoc tests are performed after a significant ANOVA result to conduct pairwise comparisons and identify exactly which groups have reliable differences between their means.
129
Which of the following statements accurately describes the null hypothesis of the Kruskal-Wallis test?
Answer:
The null hypothesis of the Kruskal-Wallis list is not that the means are the same
The Kruskal-Wallis test is a non-parametric method used to determine if there are statistically significant differences between two or more groups of an independent variable on a continuous or ordinal dependent variable. The null hypothesis states that the medians of all groups are equal, meaning the distributions are the same. Therefore, it is incorrect to state that the null hypothesis is that the means are the same.
130
Which of the following statistical parameters are considered components of a sampling distribution?
Answer:
All of these
A sampling distribution is the probability distribution of a statistic obtained through a large number of samples drawn from a specific population. Any statistical measure, such as the mean, range, or standard deviation, can be calculated for each sample. Consequently, the distribution of these calculated statistics forms a sampling distribution, making all listed options valid components.