Question

In: Statistics and Probability

The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are...

The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 42, 35, 31, 18. Assume that samples of size n=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.

42

38.5

36.5

35

33

31

30

26.5

24.5

18

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 ▼ (less than) (greater than) (equal to) the mean of the sample​ means, _______. ​(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 ▼ (do not target) (target) the population mean. In​ general, sample means ▼ (do not) (do) make good estimates of population means because the mean is ▼ (a biased) (an unbiased) estimator.

Solutions

Expert Solution

below is sampling distribution of xbar:

x1 x2 probabilityP(x1,x2)
42 42    1/16 42
42 35    1/16 38.5
42 31    1/16 36.5
42 18    1/16 30
35 42    1/16 38.5
35 35    1/16 35
35 31    1/16 33
35 18    1/16 26.5
31 42    1/16 36.5
31 35    1/16 33
31 31    1/16 31
31 18    1/16 24.5
18 42    1/16 30
18 35    1/16 26.5
18 31    1/16 24.5
18 18    1/16 18

a)

sample sample
mean probability mean probability
42    1/16 31    1/16
38.5    1/8 30    1/8
36.5    1/8 26.5    1/8
35    1/16 24.5    1/8
33    1/8 18    1/16

b)

The mean of the​ population 31.5 equal to the mean of the sample means 31.5

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

Related Solutions

The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 43,35, 22,15. Assume that samples of size n =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      Probability                               x      ...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 26, 25, 22 ,13 Assume that samples of size n=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...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 43, 25, 24, 11. Assume that samples of size n=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. x̅ Probability...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 46 comma 27 comma 21 comma 13. Assume that samples of size nequals2 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...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 33, 30, 19, 12. Assume that samples of size n=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. Xbar Probability...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are...
The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 37, 35, 31, 18. Assume that samples of size n=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...
6. The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country...
6. The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 39,35,15,14. Assume that samples of size n=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 Probability...
HW6#16 The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country...
HW6#16 The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 29, 26, 13, 11. Assume that samples of size n=2 are randomly selected with replacement from this population of four values. A. After identifying the 16 possible samples, find the mean of each sample, then construct a table representing the sampling distribution of the sample mean. B. Compare the mean of the population to the mean of the sampling distribution of the sample...
Consider the following data for a hypothetical country for 2015. Total (Billions of Dollars) Consumption 12,268...
Consider the following data for a hypothetical country for 2015. Total (Billions of Dollars) Consumption 12,268 Investment 3,018 Government Purchases 3,184 Net Exports -532 1. What is the GDP for 2015? 2. What percentage of GDP is Consumption? 3. If the population is 300 million people what is the GDP per capita in this country?
Suppose that in this particular economy, there are four assets. Assets 1, 2, and 3 are...
Suppose that in this particular economy, there are four assets. Assets 1, 2, and 3 are risky and the fourth asset is risk-free. The correlations of returns are described in the following table: Correlation Stock 1 Stock 2 Stock 3 Stock 1 1 0.6 0.7 Stock 2 0.6 1 0.2 Stock 3 0.7 0.2 1 And the standard deviation of the return of each stock is: Stock 1 0.3 Stock 2 0.6 Stock 3 0.25 Finally, the number of shares...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT