Question

Suppose that X follows a chi-square distribution with m degrees of freedom and

S=X+Y. Given that S follows a chi-square distribution with m+n degrees of freedom, and

X and Y are independent, show that Y follows a chi-square distribution with n degrees of

freedom.

Answer #1

Chi-square distribution

Suppose X follows a Chi-square distribution with degree of
freedom m = 5 so that E(X) = 5 and Var(X) = 10. Also, let Y = 4X -
10.
Find E(Y) and Var (Y).
Does Y follow a Chi-square distribution with degree of freedom m
= 10?

Suppose that χ2 follows a chi-square distribution with 6
degrees of freedom. Compute P(4≤χ2≤10). Round your answer to at
least three decimal places.
Suppose again that χ2 follows a chi-square distribution with 6
degrees of freedom. Find k such that P(χ2≥k)=0.05. Round your
answer to at least two decimal places.
Find the median of the chi-square distribution with 6 degrees
of freedom. Round your answer to at least two decimal places.
P(4≤χ2≤10)= ?
k=?
Median=?

(1) Consider a Chi-square distribution with degrees of freedom,
df =7 I What is the mean?; II. the standard deviation, for this
distribution?
(2) Consider a Chi-square distribution for a categorical
variable with 4 levels. I. What is the degrees of freedom for this
distribution? II. The chi-square test statistic was calculated to
be 8.012. What is the p-value for this distribution?

QUESTION 1
The number of degrees of freedom for the appropriate chi-square
distribution in goodness of fit test is
A
n − 1
B
(r-1)(c-1)
C
a chi-square distribution is not used
D
k − 1
QUESTION 2
A goodness of fit test and test of independence is always
conducted as a
A
upper-tail test
B
left-tail test
C
middle test
D
lower-tail test
QUESTION 3
The number of degrees of freedom for the appropriate chi-square
distribution in a test...

find the a=.05 critical value for the chi-square distribution with
8 degrees of freedom

Let X1, ..., X65 are a random sample from
chi-square distribution with 14 degrees of freedom.
1. What is the exact distribution of
X1 + ... + X65? State the name and the value
of the parameter
2. What is the approximate distribution of
X1 + ... + X65? State the name and the value
of the parameter

For a chi-square goodness-of-fit test,
what is the number of degrees of freedom, if the number of
categories in the distribution is 9? ______________
what is the critical value for a 1% level of significance?
_____________

Practice finding degrees of freedom for a Chi-square test.
Goodness of fit
categories - 1
Independence
(rows -1)( columns -1)
Homogeneity
categories -1
Variance
n-1
To look up a p-value for Chi-Square test you need to know the
degrees of freedom.
A goodness of fit test has 7 categories. What degrees of freedom
do you use?
A test for homogeneity has 9 categories. What is the degrees of
freedom, d.f.?
A test for independence has 3 rows and 9 columns....

Use the given information to find the number of degrees of
freedom, the critical values chi Subscript Upper L Superscript 2
and chi Subscript Upper R Superscript 2, and the confidence
interval estimate of sigma. It is reasonable to assume that a
simple random sample has been selected from a population with a
normal distribution.
Nicotine in menthol cigarettes 99% confidence; n=23, s=0.27 mg.
Use the given information to find the number of degrees of
freedom, the critical values chi...

The middle 0.95 portion of the chi-square distribution with 10
degrees of freedom has table values of:
a.
3.25, 18.31, respectively.
b.
2.56, 3.25, respectively.
c.
4.37, 23.84, respectively.
d.
3.25, 20.48, respectively.
e.
3.94, 20.48, respectively.

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