1) Three randomly selected households are surveyed. The numbers
of people in the households are 2, 7, and 12. Assume that samples
of size nequals2 are randomly selected with replacement from the
population of 2, 7, and 12. Construct a probability distribution
table that describes the sampling distribution of the proportion of
even numbers when samples of sizes nequals2 are randomly selected.
Does the mean of the sample proportions equal the proportion of
even numbers in the population? Do the sample proportions target
the value of the population proportion? Does the sample proportion
make a good estimator of the population proportion? Listed below
are the nine possible samples.
2,2 2,7 2,12 7,2 7,7 7,12 12,2 12,7 12,12
Construct the probability distribution table.
Sample Proportion Probability
(Type an integer or fraction.)
2) The assets (in billions of dollars) of the four wealthiest people in a particular country are 31 comma 27 comma 17 comma 11. 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 combined.
x probaility x probability
31 21
29 19
27 17
24 14
22 11
(Type integers or fractions.)
1)
since there are 9 samples and each one occur with equal probability of 1/9
| sample proportion | probability | |
| 0 | 1/9 | |
| 0.5 | 4/9 | |
| 1 | 4/9 | |
2)
| sample | sample | |||
| mean | probability | mean | probability | |
| 31 | 1/16 | 21 | 1/8 | |
| 29 | 1/8 | 19 | 1/8 | |
| 27 | 1/16 | 17 | 1/16 | |
| 24 | 1/8 | 14 | 1/8 | |
| 22 | 1/8 | 11 | 1/16 |
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