Answered: It is claimed that the median for the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

-5
It is claimed that the median for the success grade of the risk management course is less than 60 points. The scores of 6 randomly selected students;
87 77 75 65 55 54
test the hypothesis at α=0.05 significance level.

a)
Ho is accepted. Success grade is 60.

B)
Ho is rejected. Success grade is less than 60

NS)
None

D)
Ho is rejected. Success grade is 60.

TO)
Ho is accepted. Success grade is less than 60.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Expert Solution

Step 1

The claim is that median for success grade of the risk management course is less than 60 points.
Level of significance is $α = 0.05$
The given data of 6 scores are shown below
87 77 75 65 55 54

The null and alternate hypothesis are shown below
$H_{0} : M e d i a n = 60 H_{1} : M e d i a n < 60$

The data points less than 60 are given negative sign and data points greater than 60 are given positive sign as shown below
$\begin{matrix} D a t a & S i g n \\ 87 & + \\ 77 & + \\ 75 & + \\ 65 & + \\ 55 & - \\ 54 & - \end{matrix}$
The number of positive sign $= 4$
The number of negative sign $= 2$