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.
f ( x
1
, x
2
) =
2 π
√
1
2 × 3
× exp −
1
2
( x
1
− 10
2
)
2
+ ( x
1
− 20
3
)
2
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
24
4.90065934
0.16249809
-0.53298
577.002416
3.31584132
Sum Weights
Sum Observations
Variance
Kurtosis
Corrected SS
Std Error Mean
Stem Leaf
51 8
50 0344679
49 013359
48 11999
47
46 3359
45 8
----+----+----+----+
Multiply Stem.Leaf by 10**-1
4
1
#
1
7
6
5
24
117.615824
0.02640563
-0.5642116
0.60732945
0.03316978
Boxplot
|
+-----+
*--+--*
+-----+
|
|
|
1

4.
(3pts) Calculate the T
2
= n ( ¯ − µ
0
" #
)
0
9 and a hypothesized mean
5
S
− 1 n − 1
( ¯ − µ
0
) statistic from the following sample values given n = 3
¯
=
"
8
6
#
S
− 1
=
"
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) H o 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