Question
In: Statistics and Probability
In estimating the average price of a gallon of gasoline in a region we plan to...
In estimating the average price of a gallon of gasoline in a region we plan to select a random sample (independent and identically distributed) of size 10. Let X1, X2, ... , X10 denote the selected sample. The two estimators for estimating the average price, μ , are:
U1 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 +X9 + X10)/10
U2 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 )/8 + X1 - X2 .
a. which of the above estimators are unbiased? Fully justify your answer.
b. Using the mean square error criterion, determine which estimator is better.
Solutions
orchestra answered 1 year agoRelated Solutions
In estimating the average price of a gallon of gasoline in a region we plan to...
In estimating the average price of a gallon of gasoline in a
region we plan to select a random sample (independent and
identically distributed) of size 10. Let X1 , X2 , ... , X10 denote
the selected sample. The four estimators for estimating the average
price, mu, are:
U1 = ( X1 + X2 + ... + X10 ) /10
U2 = ( X1 + X2 + ... + X8 ) /8 + X10 - X9
U3 = (...
In estimating the average price of a gallon of gasoline in a region we plan to...
In estimating the average price of a gallon of gasoline in a
region we plan to select a random sample (independent and
identically distributed) of size 10. Let X1,
X2, ... , X10 denote the selected sample. The
two estimators for estimating the average price, μ, are:
U1 = (X1 + X2 + X3 +
X4 + X5 + X6 + X7 +
X8 +X9 + X10)/10
U2 = (X1 + X2 + X3 +
X4 + X5 + X6...
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1.
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1976 price to constant 1998 dollars. Was gas more expensive in 1976
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Oil and Gas Prices The average gasoline price per gallon (in cities) and the cost of...
Oil and Gas Prices The average gasoline price
per gallon (in cities) and the cost of a barrel of oil are shown
below for a random selection of weeks in
2015
.
Oil (
$
)
Gasoline (
$
)
55.78
2.654
41.96
2.269
52.08
2.445
57.28
2.710
58.15
2.805
67.59
3.071
The correlation coefficient for the data is
=r0.978
and
=α0.01
. Should regression analysis be done?
The regression
analysis should not be done.
The regression
analysis should be...
Oil and Gas Prices The average gasoline price per gallon (in cities) and the cost of...
Oil and Gas Prices The average gasoline price per gallon (in
cities) and the cost of a barrel of oil are shown below for a
random selection of weeks in 2015. Oil ($) Gasoline ($) 55.78 2.654
41.96 2.269 52.08 2.445 57.28 2.710 58.15 2.805 67.59 3.071
Oil and Gas Prices The average gasoline price per gallon (in cities) and the cost of...
Oil and Gas Prices The average gasoline price
per gallon (in cities) and the cost of a barrel of oil are shown
below for a random selection of weeks from 2015.
Oil
$47.79
$44.62
$81.08
$43.67
$40.58
$48.64
Gasoline
2.638
2.636
2.944
2.528
2.623
2.682
1) The correlation coefficient for the data is r =
0.951 and a = 0.01. Should regression analysis be
done?
a) The regression analysis should not be done or b) The
regression analysis should be...
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