Determine ​(a) the χ20 test​ statistic, ​(b) the degrees of​ freedom, ​(c) the​ P-value, and ​(d) test the hypothesis at the α=0.05 level of significance.   X 0 1 2 3 4   Observed 2 39 124 441 389   Expected 1.6 25.5 152.8 407.6 407.6     H0​: The random variable X is binomial with n=4​, p=0.8 H1​: The random variable X is not binomial with n=4​, p=

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Determine ​(a) the
χ20
test​ statistic, ​(b) the degrees of​ freedom, ​(c) the​ P-value, and ​(d) test the hypothesis at the
α=0.05
level of significance.
 
X
0
1
2
3
4
 
Observed
2
39
124
441
389
 
Expected
1.6
25.5
152.8
407.6
407.6
 
 
H0​:
The random variable X is binomial with
n=4​,
p=0.8
H1​:
The random variable X is not binomial with
n=4​,
p=
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