The frequency distribution shows the results of 200 test scores. Are the test sc
ID: 3229334 • Letter: T
Question
The frequency distribution shows the results of 200 test scores. Are the test scores nomnaly distributed? Use o 30.01 Complete parts (a) through (dL 495-58.5 58 567 67.5-76.5 76 5-85.5 85 5-94.5 20 Using a chi square goodness-of-fittest, you can decide, with some degree of certainty. whether a variable is normally distributed. In all chi-square tests for normality, the null and alternative hypotheses are as follows. Ho: The test scores have a normal distribution. Ha The test scores do not have a normal distribution. a. Find the expected frequencies. Class boundaries 495 585 58.5675 675 7615 5.855 B55945 requency f pected frequency (Round to the nearest integer as needed.) b. Determine the critical value, X0, and the rejection region. xo- Round to three decimal places as needed. Click to select your answers).Explanation / Answer
Part-a-From Following results we found expected frequencies as Ei
Class Boundary
f
Mid Point x
fx
fx^2
Zi=(Upper Bound-69.39)/8.40
P(Z<zi)
p=P(In the class interval)
Expected Frequency=200*p
(Oi-Ei)^2/Ei
49.5-58.5
20
54
1080
58320
-1.30
0.10
0.10
19.48
0.01
58.5-67.5
60
63
3780
238140
-0.23
0.41
0.31
62.72
0.12
67.5-76.5
82
72
5904
425088
0.85
0.80
0.39
78.07
0.20
76.5-85.5
34
81
2754
223074
1.92
0.97
0.17
34.22
0.00
85.5-94.5
4
90
360
32400
2.99
1.00
0.03
5.23
0.29
Total
200
360
13878
977022
4.23
3.28
1.00
199.72
0.621
Mean=13878/200
69.39
SD
8.40
Part-b
Degree of freedom=k-1=5-1=4
Critical values 02= 13.277 using excel function =CHIINV(0.01,4)
Critical Region is values 2 > 02-option-A
Part-c
From above table test statistic 2=0.621
Part-d
Do not reject H0. At 1% significance level there is no enough evidence to reject the the claim that test scores are normally distributed
Class Boundary
f
Mid Point x
fx
fx^2
Zi=(Upper Bound-69.39)/8.40
P(Z<zi)
p=P(In the class interval)
Expected Frequency=200*p
(Oi-Ei)^2/Ei
49.5-58.5
20
54
1080
58320
-1.30
0.10
0.10
19.48
0.01
58.5-67.5
60
63
3780
238140
-0.23
0.41
0.31
62.72
0.12
67.5-76.5
82
72
5904
425088
0.85
0.80
0.39
78.07
0.20
76.5-85.5
34
81
2754
223074
1.92
0.97
0.17
34.22
0.00
85.5-94.5
4
90
360
32400
2.99
1.00
0.03
5.23
0.29
Total
200
360
13878
977022
4.23
3.28
1.00
199.72
0.621
Mean=13878/200
69.39
SD
8.40
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