Test your knowledge of permutations and combinations with this interactive quiz! The MCQs Permutations Combinations Quiz covers essential concepts like factorials, combinations, arrangements, and real-world applications. This quiz is perfect for students and enthusiasts looking to sharpen their probability and counting skills. Let us start with the MCQs Permutation Combinations Quiz now.
Online Quiz about Permutations and Combinations with Answers
Online MCQs Permutations Combinations
The number of ways to select 2 persons from 6, ignoring the order of selection, is
$n!=$?
An arrangement of all or some of a set of objects in a definite order is called
An arrangement of objects without caring for the order is called
${}^nP_r$ =
${}^nC_r$ =
In how many ways can a team of 6 players be chosen from 11 persons
How many terms are in the expansion of the $(q+p)^n$
${}^{10}C_5=$
${}^5C_5$ is equal to
The difference between permutation and combination lies in the fact that
Which of the following statements is true?
A homeowner doing some remodeling requires the services of both a plumbing contractor and an electrical contractor. If there are 15 plumbing contractors and 10 electrical contractors available in the area, in how many ways can the contractors be chosen?
How many permutations of size 3 can be constructed from the set (A, B, C, D, E)?
How many combinations of size 4 can be formed from a set of 6 distinct objects?
An experiment consists of three stages. There are five ways to accomplish the first stage, four ways to accomplish the second stage, and three ways to accomplish the third stage. The total number of ways to accomplish the experiment is
The $0!$ is
In how many ways can be letters in the word UNIVERSITY be arranged randomly
Seventeen teams can take part in the Football Championship of a country. In how many ways can the Gold, Silver, and Bronze medals be distributed among the teams?
The number of 3-digit telephone area codes that can be made if repetitions are not allowed is
Test your econometrics knowledge with this comprehensive Econometrics Quiz and Answers MCQs Test! Perfect for statisticians and econometricians preparing for exams or job interviews. Covers measurement errors, multicollinearity, heteroscedasticity, dummy variables, VIF, and more. Check your understanding of key concepts in Econometrics today! Let us start with the Online Econometrics Quiz and Answers now.
Understand the sampling distribution of differences between means—what it is, why it matters, and how to apply it in hypothesis testing (with examples). Perfect for students, data scientists, and analysts! Ever wondered how statisticians compare two groups (e.g., test scores, sales performance, or medical treatments)? The key lies in the sampling distribution of differences between means—a fundamental concept for hypothesis testing, confidence intervals, and A/B testing.
Table of Contents
Sampling Distribution of Differences Between Means
The Sampling Distribution of Differences Between Means is the probability distribution of differences between two sample means (e.g., $Mean_A – Mean_B$) if you repeatedly sampled from two populations.
Let there are two populations of size $N_1$ and $N_2$ having means $\mu_1$ and $\mu_2$ with variances $\sigma_1^2$ and $\sigma_2^2$. We need to draw all possible samples of size $n_1$ from the first population and $n_2$ from the second population, with or without replacement.
Let $\overline{x}_1$ be the means/averages of samples of the first population and $\overline{x}_2$ be the means/averages of the samples of the second population. After this, we will determine all possible differences between means/averages denoted by $$d =\overline{x}_1 – \overline{x}_2$$
We call the frequency distribution differences as frequency distribution, while the probability distribution of the differences is the sampling distribution of differences between means.
Notations for Sampling Distribution of Differences between Means
Notation
Short Description
$\mu_1$
Mean of the first population
$\mu_2$
Mean of the second population
$\sigma_1^2$
Variance of the first population
$\sigma_2^2$
Variance of the second population
$\sigma_1$
Standard deviation of the first population
$\sigma_2$
Standard deviation of the second population
$\mu_{\overline{x}_1 – \overline{x}_2}$
Mean of the sampling distribution of difference between means
$\sigma^2_{\overline{x}_1 – \overline{x}_2}$
Variance of the sampling distribution of difference between means
$\sigma_{\overline{x}_1 – \overline{x}_2}$
Standard deviation of the sampling distribution of difference between means
Some Formulas for Sampling with/without Replacement
Let $\overline{x}$ represent the mean of a sample of size $n_1=2$ selected at random with replacement from a finite population consisting of values 5, 7, and 9. Similarly, let $\overline{x}_2$ represent the mean of a sample of size $n_2=2$ selected at random from another finite population consisting of values 4, 6, and 8. Form the sampling distribution of the random variable $\overline{x}_1 – \overline{x}_2$ and verify that