## MCQs Design of Experiments

This test contains multiple-choice questions from Design of Experiments (DOE).

MCQs DOE 3 | MCQs DOE 2 | MCQs DOE 1 |

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# Author: Muhammad Imdad Ullah

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MCQs Design of Experiments

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MCQs DOE 2

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MCQs Random Variable

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Wilcoxon Signed Rank Test

Basic Statistics and Data Analysis

Statistics Lecture Notes, Online MCQs

This test contains multiple-choice questions from Design of Experiments (DOE).

MCQs DOE 3 | MCQs DOE 2 | MCQs DOE 1 |

Multiple Choice Questions about the Design of Experiments for preparation of examinations related to PPSC, FPSC, NTS, and Statistics job- and education-related examinations

The following are online quizzes containing MCQs about Random variable.

Start any of the online quizzes/exams/tests by clicking the links below.

MCQs Random Variable 6 | MCQs Random Variable 5 | MCQs Random Variable 4 |

MCQs Random Variable 3 | MCQs Random Variable 2 | MCQs Random Variable 1 |

A Random Variable (random quantity or stochastic variable) is a set of possible values from a random experiment. The domain of a random variable is called sample space. For example, in the case of a coin toss experiment, there are only two possible outcomes, namely heads or tails. A random variable can be either discrete or continuous. The discrete random variable takes only certain values such as 1, 2, 3, etc., and a continuous random variable can take any value within a range such as the height of persons.

The Wilcoxon Signed Rank test assumes that the population of interest is both continuous and symmetric (not necessarily normal). Since the mean and median are the same (for symmetrical distribution), the hypothesis tests on the median are the same as the hypothesis test on the mean.

The Wilcoxon test is performed by ranking the non-zero deviations in order of increasing magnitude (that is, the smallest non-zero deviation has a rank of 1 and the largest deviation has a rank of $n$). The ranks of the deviations with positive and negative values are summed.

These sums are used to determine whether or not the deviations are significantly different from zero. Wilcoxon Signed Rank Test is an alternative to the Paired Sample t-test.

**One-Tailed Test**

$H_0: \mu = \mu_0\quad $ vs $\quad H_1: \mu < \mu_0$

Test Statistics: $T^-$: an absolute value of the sum of the negative ranks

**Two-tailed Test**

$H_0: \mu = \mu_0 \quad$ vs $\quad H_1:\mu \ne \mu_0$

Test Statistics: $min(T^+, T^-)$

Because the underlying population is assumed to be continuous, ties are theoretically impossible, however, in practice ties can exist, especially if the data has only a couple of significant digits.

Two or more deviations having the same magnitude are all given the same average rank. The deviations of zero are theoretically impossible but practically possible. Any deviations of exactly zero are simply thrown out and the value of $n$ is reduced accordingly.