ST372
QUIZ 1 SAS HALL Fall 2013
Ver. A
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Problem 1: The t distribution gets closer to the normal distribution as
a.
b.
c.
d.
e.
the median minus the mean becomes positive
the sample size increases
the sample mean gets closer to zero
the sample standard deviation decreases
none of the above
Problem 2: What is the correct form of a 100(1   )% SMALL-SAMPLE TWO-SIDED
confidence interval for 
A. X  ( z )(s / n )
B. X  ( z / 2 )(s / n )
C. X  (t ,n1 )( s / n )
D. X  (t / 2,n1 )( s / n )
E. none of these
Problem 3: Establish the probability that the computed t value with degrees of freedom = 14
will fall below 2.977
a) .90
b) .10
c) .995
d) .20
e) .005
Problem 4: If the form for a LARGE SAMPLE two-sided confidence interval for  is given
by X  2.33(s / n ) , what is the level of confidence?
A. 99.5 %
B. 99 %
C. 96 %
D. 97 %
E. 98%
Problem 5: if the value of the MAXIMUM LIKELIHOOD estimate of the parameter  is 7,
Then the maximum likelihood estimate of  3 is 343.
False
True
CANNOT BE DETERMINED FROM DATA GIVEN
1
PROBLEMS 6 & 7: Suppose X1 , X 2 , X 3 and X 4 are INDEPENDENT random variables with
means of: E[ X1 ] = 3 , E[ X 2 ] = 4 , E[ X 3 ] = 5 and E[ X 4 ] = 6
with variances Var[ X1 ] = 3 , Var[ X 2 ] = 5 , Var[ X 3 ] = 7 and Var[ X 4 ] = 10
Let Y = -7 -2 X1 +
4 X2 - X3
+ 5 X4
Problem 6: Find the mean or expected value of Y
a) 28
b) 57
c) 35
d) 42
e)
64
Problem 7: Find the variance of Y
a) 83
b) 57
c) 349
d) 257
e) 311
Problem 8: If the level of confidence is kept constant, say at 95 %, what happens to the
WIDTH of a confidence interval for  as n increases
a. it could increase or decrease, depending on the value of X
b. it remains the same
c. it decreases
d. it increases
e. there is not enough information to answer the question
Problem 9: Suppose that we want a 95% two-sided confidence interval for p = proportion of
defectives if we observe 7 defectives in 60 items tested (to 3 decimals).
a. (.049, .185)
b. (.036, .198) c. (.004, .130) d. (.077, .157) e. (.113,.120)
Problem 10: Find the LOWER limit of the two-sided 95% confidence intervals for  , given
the following sample results: sample Mean = 90.70, sample Variance = 1.5, n=10.
NOTE you are given VARIANCE not the standard deviation.
a) 91.6
b) 89.8
c) 91.3
d) 92.7
e) 90.90
Problem 11: For the data in problem 10: sample Mean = 90.70, sample Variance = 1.5,
n=10, a TWO sided 98% Confidence interval for  2 is:
a) (.6777,2.3223)
b) (.9887,6.2366)
c) (1.0646,7.5000)
d) (.7097,5.000)
e) (.6231,6.4655)
Problem 12: For the data in problem 10: sample Mean = 90.70, sample Variance = 1.5,
n=10, the LOWER LIMIT of a TWO SIDED TOLERANCE INTERVAL for capturing AT
LEAST 95% of the values with a confidence level of 99% is
a) 97.10
b) 85.48
c) 95.92
d) 84.30
e) 96.13
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Problem 13: We are studying a population with unknown mean  and a standard deviation 
that we guess is around 2. We plan to take a random sample and want to construct a 99.9 % twosided confidence interval of length 1.92 (right endpoint MINUS left endpoint = 1.92). How large
should the sample size be?
a. 34
b. 5
c. 19
d. 47
e. 12
Problem 14: Over the past 27 years, the Lizard Lick Candy Company has produced an average
of 57.0 pounds of jalapeño hedgehog birthday cake mix for Washington politicians each day.
The records show that for the current year, based on 221 operating days The following
information was obtained
Sample mean X = 55.60 pounds/day
Sample standard deviation s = 2.1 pounds/ day
A
99% two-sided confidence interval for the sample mean of the current year
a)
b)
c)
d)
e)
(55.27, 55.93)
(55.24, 55.96)
(54.30, 56.90)
(56.64, 57.36)
(56.67, 57.33)
is
Problem 15: For the same data in problem 10,
A 98% ONE-sided LOWER confidence interval for the sample mean of the current year is
b) (,55.89)
a) (54.30,56.90)
c) (55.31, )
d) (,60.39) e) (50.81, )
Problem 16- 18: Suppose X 1 , , X n is a random sample from the GAMMA DENSITY
f(x;  ) =
1
x e  x /  , for 0  x  ,   0
2
Note: in the yellow table book the gamma density and mean and variance are given.
with pdf given as
Problem 16: The Method of Moments estimator of  is
a) 3 X
b) 3/ X
c) X / 2
d) X / 3
e) none of these
Problem 17: The Maximum Likelihood estimator of  is
a) X / 2
b) X / 3
c) 3 X
d) 3/ X
e) none of these
Problem 18: The Method of Moments estimator of  is BIASED
TRUE
FALSE
depends on sample size
3
Problem 19-20: An electrical potential will be applied across a resistor. Ohm's law
predicts that in such a situation, the current, I, flowing in the circuit will be
1 

 R1 
I=V 
where R1 is the resistance and V is the potential applied. Suppose that R1
has a mean of 10 ohms and standard deviation of 0.1 ohms, and that V has a mean of 9
volts and a standard deviation of 0.2 volt.
Problem 19: Find an approximate MEAN for the current, I, treating V and R1 as
INDEPENDENT random variables
a) 180
b) 0.0225
c) 0.45
d) 0.9
e) 90
Problem 20: Find an approximate STANDARD DEVIATION for the current I, treating
V and R1 as INDEPENDENT random variables
a) 0.000105
b) 0.00041
c) 0.01025
4
d) 0.02193
e) none of these
EXTRA CREDIT: 5 points
What topic or idea are you having the most trouble with in the course thus far?
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