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stats-230 summer 2014

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Use the information below to answer Questions 1 through 3.
Given a sample size of 34, with sample mean 660.3 and sample standard deviation 104.9, we
perform the following hypothesis test. Since n>30, this is a Z test.
Null Hypothesis
0
: 700H
µ
=
Alternative Hypothesis
: 700
a
H
µ
 What is the test statistic? What is the p-value?
The test statistic is,
Test statistic =
660.3700
104.9
34
=2.2068
The p-value is,
P-value = P (|Z|>2.2068) = 0.0273
 At a 5% significance level (95% confidence level), what is the critical value(s)in this
test? Do we reject the null hypothesis?
At 5% significance level the critical value is ±Z (0.025) = ±1.96.
 What are the border values of
x
between acceptance and rejection of this hypothesis?
As the critical values are ±1.96 so the border values of
́x
are
±
1.96104.9
34
=±35.2608
Questions 4 through7involve rolling of dice.
 Given a fair, six-sided die, what is the probability of rolling the die twice and getting a
“1” each time?
As both dice throws are independent so the required probability would be the
multiplication of probabilities of getting 1 in the 1
st
and 1 in the 2
nd
throw.
So the required probability = 1/6*1/6 = 1/36.
 What is the probability of getting a “1” on the second roll when you get a “1” on the first
roll?
As throws are independent so getting 1 in the 2
nd
does not depend on getting 1 on the 1
st
thus the required probability is getting 1 on the 2
nd
which is 1/6.
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 The House managed to load the die in such a way that the faces “2” and “4” show up
twice as frequently as all other faces. Meanwhile, all the other faces still show up with
equal frequency. What is the probability of getting a “5” when rolling this loaded die?
There are 6 faces in a dice. 2 and 4 has double probability so the probability of getting a 5
is 1/(6+2) = 1/8.
 Write the probability distribution for this loaded die, showing each outcome and its
probability.
The probability distribution is given below,
O
u
t
c
o
m
e
P
r
o
b
a
b
il
it
y
1
1
/
8
2
1
/
4
3
1
/
8
4
1
/
4
5
1
/
8
6
1
/
8
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Use the data in the table to answer Questions 8through9.
x 3 1 4 4 5
y 2 -2 5 4 8
 Determine SS
xx
, SS
xy
, and SS
yy
.
S S
xx
=
x
2
n
(
́x
)
2
=6753.4
2
=9.2
S S
xy
=
xyn ́x ́y =8053.43.4=22.2
 Find the equation of the regression line. What is the predicted value when
4?x =
We know the regression equation is,
̂
y= ́y
S S
xy
S S
xx
́x+
S S
xy
S S
xx
x=3.4
22.2
9.2
3.4 +
22.2
9.2
x
̂
y=4.8043+2.4130x
Thus for x = 4 the predicted y is,
̂
y=4.8043+2.41304=4.8477
Use the data below to answer Questions 10 through 12.
A group of students from three universities were asked to pick their favorite college sport to
attend of their choice: The results, in number of students, are listed as follows:
Footb
all
Basketb
all
Socc
er
Total
Maryla
nd
60 70 20 150
Duke 10 75 15 100
UCLA 35 65 25 125
Total 105 210 60 375
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