Practice Questions 6
QUESTIONS 1 THROUGH 3 ARE BASED ON THE FOLLOWING INFORMATION:
Let
1
X
,
2
X
,
3
X
, and
4
X
be a random sample of observations from a population with mean
μ
and variance
2
σ
.
Consider
the following two point estimators of
μ
:
1
ˆ
θ
= 0.10
1
X
+ 0.40
2
X
+ 0.40
3
X
+ 0.10
4
X
and
2
ˆ
θ
= 0.20
1
X
+ 0.30
2
X
+ 0.30
3
X
+ 0.20
4
X
1.
Which of the following is true?
A)
1
ˆ
θ
is biased, but
2
ˆ
θ
is unbiased estimator of
μ
.
B)
1
ˆ
θ
is unbiased, but
2
ˆ
θ
is biased estimator of
μ
.
C)
Both
1
ˆ
θ
and
2
ˆ
θ
are unbiased estimators of
μ
.
D)
Both
1
ˆ
θ
and
2
ˆ
θ
are biased estimators of
μ
.
2.
Which of the following is true?
3.
Which of the following is true?
4.
In a recent survey of 600 adults, 16.4% indicated that they had fallen asleep in front of the television in the past
month. Which of the following intervals represents a 96% confidence interval for the population proportion?
5.
The amount of material used in making a custom sail for a sailboat is normally distributed.
For a random sample of
15 sails, you find that the mean amount material is 912 square feet, with a standard deviation of 64 square feet.
Which of the following represents a 99% confidence interval for the population mean amount of material used in a
custom sail?
A)
912
±
49.2
B)
912
±
42.6
C)
912
±
44.3
D)
912
±
46.8

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