Stat 407 Quiz 2 Name 1

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Stat 407
Quiz 2
Name
1. (2pts) Which of the following samples is most likely to correspond to this correlation matrix
"
#
1 0.5
?
0.5 1
2. (2pts) From this formula for a bivariate normal density tell me what the mean is and the variance of the
distribution is.
1 x1 − 10 2
x1 − 20 2
1
√
× exp −
( √
) +( √
)
2
2π 2 × 3
2
3
f (x1 , x2 ) =
3. (2pts) Based on the following SAS output, would you describe the variable LLENGTH as coming from a
normal distribution?
The UNIVARIATE Procedure
Variable: LLength
Moments
N
Mean
Std Deviation
Skewness
Uncorrected SS
Coeff Variation
Stem
51
50
49
48
47
46
45
24
4.90065934
0.16249809
-0.53298
577.002416
3.31584132
Sum Weights
Sum Observations
Variance
Kurtosis
Corrected SS
Std Error Mean
Leaf
8
0344679
013359
11999
#
1
7
6
5
3359
4
8
1
----+----+----+----+
Multiply Stem.Leaf by 10**-1
1
24
117.615824
0.02640563
-0.5642116
0.60732945
0.03316978
Boxplot
|
+-----+
*--+--*
+-----+
|
|
|
4. (3pts) Calculate the T 2 = "n(X̄#− µ0 )0 S−1
n−1 (X̄ − µ0 ) statistic from the following sample values given n = 3
9
and a hypothesized mean
5
X̄ =
"
8
6
#
−1
S
=
"
1/3 1/9
1/9 4/27
#
Would you reject the null hypothesis?
5. (1pt) Which of the following is NOT an assumption underlying the contruction of the test statistic when
testing hypotheses about the multivariate mean (such as in the previous question)?
(a) Ho is true.
(b) The sample is taken by simple random sampling methods.
(c) The variance-covariance matrices are equal.
(d) The population takes a multivariate normal shape.
2
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