Answered: Test to see if these two variables…

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

1. Test to see if these two variables (type of Masters program and whether graduates from these programs are continuing in a Ph.D. program) are related. Numbers in each cell represent frequencies (i.e., the number of people).

		Masters Program
		A	B	C
Admitted to	Yes	20	9	11
Ph.D. Program	No	17	22	21

Expert Solution

Step 1

Hypothesis:

$H_{0} :$ There is no association between type of Masters program and whether graduates from these programs are continuing in a Ph.D. program.

$H_{1} :$ There is association between type of Masters program and whether graduates from these programs are continuing in a Ph.D. program.

Calculation:

Observed frequency:

The observed frequencies are given in the table below:

Admitted to Ph.D program		Master's program
	A	B	C	Row total
Yes	20	9	11	40
No	17	22	21	60
Column Total	37	31	32	100

Step 2

Expected frequency:

The table below shows the expected frequencies calculated using formula,

$E = \frac{R o w t o t a l \times C o l u m n t o t a l}{G r a n d t o t a l}$

Admitted to Ph.D program		Master's program
	A	B	C
Yes	$14.80 (= \frac{40 \times 37}{100})$	$12.40 (= \frac{40 \times 31}{100})$	$12.80 (= \frac{40 \times 32}{100})$
No	$22.20 (= \frac{60 \times 37}{100})$	$18.60 (= \frac{60 \times 31}{100})$	$19.20 (= \frac{60 \times 32}{100})$

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