The assets (in billions of dollars) of the four wealthiest people in a particula
ID: 3358008 • Letter: T
Question
The assets (in billions of dollars) of the four wealthiest people in a particular country are 39, 30, 23, 15.
Assume that samples of size
nequals=2
are randomly selected with replacement from this population of four values.
a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distribution of the sample mean. In the table, values of the sample mean that are the same have been combined.
x overbarx
Probability
x overbarx
Probability
39
26.5
34.5
23
31
22.5
30
19
27
15
(Type integers or fractions.)
b. Compare the mean of the population to the mean of the sampling distribution of the sample mean.
The mean of the population,
nothing,
is
(1)
the mean of the sample means,
nothing.
(Round to two decimal places as needed.)
c. Do the sample means target the value of the population mean? In general, do sample means make good estimates of population means? Why or why not?
The sample means
(2)
the population mean. In general, sample means
(3)
make good estimates of population means because the mean is
(4)
estimator.
(1)
greater than
less than
equal to
(2)
target
do not target
(3)
do not
do
(4)
a biased
an unbiased
x overbarx
Probability
x overbarx
Probability
39
26.5
34.5
23
31
22.5
30
19
27
15
Explanation / Answer
a) as each sample has equal probability of drawing therefore probability of each sample =1/16
from above below is sampling distribution of mean:
b)
mean of the population equal to
mean of the sample means (26.75
c)
The sample means target the population mean. In general, sample means do make good estimates of population means because the mean is an unbiased estimator.
x1 x2 Xbar P(Xbar) 39 39 39 1/16 30 39 34.5 1/16 23 39 31 1/16 15 39 27 1/16 39 30 34.5 1/16 30 30 30 1/16 23 30 26.5 1/16 15 30 22.5 1/16 39 23 31 1/16 30 23 26.5 1/16 23 23 23 1/16 15 23 19 1/16 39 15 27 1/16 30 15 22.5 1/16 23 15 19 1/16 15 15 15 1/16Related Questions
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