Statistics MCQs
Topic Notes: Statistics
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
In statistical hypothesis testing, what is the conventional threshold for defining a 'small' sample size?
Answer:
n < 30
In classical statistics, a sample size of n < 30 is generally considered small, often necessitating the use of the t-distribution for hypothesis testing regarding means. When n is 30 or larger, the Central Limit Theorem allows for the use of the normal distribution (Z-test) as an approximation.
2
Under what condition does the distribution of the difference between two proportions approximate a standard normal distribution?
Answer:
n > or = 30
The normal approximation for the difference of proportions is generally considered valid when the sample sizes are sufficiently large, typically defined by the rule of thumb where n is at least 30, or more strictly, when the expected number of successes and failures in both groups is at least 5 or 10. This allows the use of Z-tests for comparing proportions.
3
Which of the following is a fundamental assumption for using the t-distribution in statistical inference?
Answer:
The sample are drawn from a normally distributed population.
A key assumption for the validity of the t-distribution in hypothesis testing is that the underlying population from which the sample is drawn follows a normal distribution. While the t-test is robust to minor deviations from normality, this assumption is central to the derivation of the t-statistic.
4
How does an increase in sample size influence the characteristics of the t-distribution?
Answer:
All Above
As sample size increases, the standard error of the mean decreases, the degrees of freedom increase (which makes the t-distribution approach the standard normal distribution), and the precision of the t-ratio improves. All these components are fundamentally affected by the sample size in statistical inference.
5
What is the shape characteristic of the t-distribution?
Answer:
Symmetrical
Like the standard normal distribution, the t-distribution is perfectly symmetrical around its mean, which is zero. However, it is distinguished by having 'thicker' or 'heavier' tails, which account for the additional uncertainty when estimating population parameters from smaller sample sizes.
6
How does the t-distribution compare to the standard normal distribution as the degrees of freedom increase?
Answer:
Greater the degree of freedom, the more the t-distribution resembles the standard normal distribution
The t-distribution is characterized by heavier tails than the standard normal distribution. As the degrees of freedom increase, the t-distribution's variance decreases, and its shape converges toward the standard normal distribution, eventually becoming identical as degrees of freedom approach infinity.