Assume that random variable x^2 has a chi-squared distribution
with v degree of freedom. Find the value of “A” for the following
cases
1) P(X^2 <=A) =.95 when v = 6
2) P(X^2>=A) =.01 when v = 21
3) P(A <= X^2 <= 23.21)= .015 when v = 10.
What is the critical value for a chi-square test with 13 degrees
of freedom at the 1 percent level of significance? If the
chi-square test statistic were 16.98, what would you conclude
regarding the null hypothesis? What would you conclude if the
chi-square value were 68.03? (30 points)
Find the critical values chi squared Subscript Upper Lχ2L and
chi squared Subscript Upper Rχ2R for the given confidence level c
and sample size n. cequals=0.980.98, nequals=2626 chi squared
Subscript Upper Lχ2Lequals=nothing (Round to three decimal places
as needed.)
For each chi-square test statistic and degree of freedom from
some data, provide the p-value by reading off from a table or using
a computer program (closest value on the table is sufficient,
provide 3 decimal points, i.e., 0.XXX format).
a. Chi-square statistic: 12.5 (df = 3)
b. Chi-square statistic: 12.5 (df = 5)
c. Chi-square statistic: 66.8 (df = 40)
State the critical value of ?2 and determine the
appropriate conclusion for a chi-square test for
association using the given information.
a) ? = 0.025, Number of rows = 5, Number of columns = 5, ?2 =
31.1
b) ? = 0.10, Number of rows = 7, Number of columns = 6, ?2 =
40.3
Let X1 and X2 be two independent random
variables having a chi-squared distribution with degrees of freedom
n1 and n2, respectively. Let
Y1 = (X1) / (X1 + X2)
and Y2 = X1 + X2
(a) Find the joint p.d.f. of Y1 and Y2
(b) Find the marginal p.d.f. of each of Y1 and
Y2
(c) Are Y1 and Y2 independent ?
Justify your answer.
Determine (a) the χ2 test statistic, (b) the
degrees of freedom, (c) the critical value using
alpha equals 0.05α=0.05, and (d) test the hypothesis at the
alpha equals 0.05α=0.05
level of significance.
Ho:Pa=Pb=Pc=Pd=1/4
H1: At least one of the proportions is different from the
others.
Outcome
A
B
C
D
Observed
52
47
53
48
Expected
50
50
50
50