MS Model
MS Error
2
2
T
M
s
s
2
2
1
ln
2
M
E
s
s
SSM
SSE
have for this hypothesis test?
6.12
How many degrees of freedom would the tstatistic
Practice Quiz 3
11
6.13
What is the critical value for this ttest?
6.15
Do you get the same results from the ttest and the Ftest?
6.16
Why?
Practice Quiz 3
12
Problem 7
Cross tabulated count data
A recent poll surveyed a simple random sample of 100 voters in Washington. Respondents were classified by age group
and voting behavior. Use the following results to test the hypothesis that age is independent of voting behavior.
OBSERVED
Voted
Did not vote
Total
18 to 28
25
75
29 to 45
50
50
>45
75
25
Total
150
150
7.1
What is the general formula for the expected value of the cell counts under the null hypothesis that voting status is
independent of age?
?(?
??
) =
?
+?
?
?+
?
++
Work out the expected values in this table under the null hypothesis that age is independent of voting preference.
Show
both the formula with plug in values, and solve for the answer. (7.27.7)
EXPECTED
Voted
Did not vote
Total
18 to 28
7.2
50
7.3
50
100
29 to 45
7.4
50
7.5
50
100
>45
7.6
50
7.7
50
100
Total
150
150
7.8
What is the general formula for the contribution of each cell to the Chisquared statistic?
?
??
2
=
(?
??
− ?
??
)
2
?
??
100
100
100
300
300
Practice Quiz 3
13
Work out the squared standardized residuals (
z
ij
2
) in this table
(7.97.14)
z
ij
2
Voted
Did not vote
18 to 28
7.9
12.5
7.10
12.5
29 to 45
7.11
0
7.12
0
>45
7.13
12.5
7.14
12.5
7.15
What is the value of the Chisquare statistic for
7.16
How many degrees of freedom does the Chi
square statistic for this test have?
Show the
formula with plug in values and the result
7.17
What is the α=0.05 critical value of the Chi

𝜒
𝜒
8.
Basic questions about statistical inference
8.1
The central limit theorem in
statistics is used to make
inferences about
a.
The distribution of a discrete random variable
b.
The sampling distribution of a sample mean
c.
The variance of a sample of size n
d.
The exponential approximation for a Normal distribution
e.
None of the above
8.2
Pvalues in hypothesis tests for
a sample mean of the random
variable X are based on
Practice Quiz 3
14