Problem 2: Three candidates for deanship in a college were voted on by 75 faculty members. The result is shown below. Test whether the candidates are equally preferred. Use 0.01 and 0.05 level. Candidate Y Observed 13 34 28 Expected 15 25 25
Problem 2: Three candidates for deanship in a college were voted on by 75 faculty members. The result is shown below. Test whether the candidates are equally preferred. Use 0.01 and 0.05 level. Candidate Y Observed 13 34 28 Expected 15 25 25
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Test of goodness of fit.
Answer the first picture just like how the second picture is answered
Transcribed Image Text:Example 1
After 100 tosses of a coin, 44 came out heads and 56 tails. As expected, based on theory, they should come out 50/50.
Heads
Tails
Observed (O)
44
56
Expected (E)
50
50
(44 – 50) (56– 50)
Ho: The coin is not biased.
Ha: The coin is biased.
.(0- E}
x² ==
50
50
%3D
E
(-6) (6)
df = (I – 1)(J – 1)
50
50
1.44 <
3.84
Ассept
The coin is not biased.
36 36
Re
На.
(I-1)(J-1)
0.05
+
%3D
50 50
x´(2-1)(2–1)
0.05
72
0.05 -x
= 3.84
50
x? =1.44
Example 2
90 qualified high school graduates are asked which of three universities they prefer. The result is shown below.
School X
School Y
School Z
Observed (O)
18
38
34
Expected (E)
30
30
30
(18–30) (38– 30) (34– 30)
.(0 - E)} x²
x² =E
Ho: There is no significant difference in the
preference of the students in the three
universities.
+
30
30
30
E
(-12) (8) (4)°
Ha: Ho: There is no significant difference
in the preference of the students in the
df = (I – 1)(J – 1)
30
30
30
three universities.
144 64 16
0.05
(1-1)(J-1)
+
30 30
%3D
30
7.47 >
5.99
0.05 X (2–1)(3–1)
224
Accept Ha, Reject Ho.
There is a significant difference in the preference of the
30
0.05 X2 = 5.99
x' = 7.47
students in the three universities.
LIDESMANIA.C
LIDESMANIA.C
Transcribed Image Text:Problem 1: A die is rolled 60 times. The spots 1 to 6 are recorded below. Test the
biasness of the die using 0.01 and 0.05 level.
Spot
1
2
Observed
12
8
15
14
Expected
10
10
10
10
10
10
Problem 2: Three candidates for deanship in a college were voted on by 75 faculty
members. The result is shown below. Test whether the candidates are equally
preferred. Use 0.01 and 0.05 level.
Candidate
Y
Observed
13
34
28
Expected
15
25
25
LIDESMANIA.C
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