Question
Suppose that a random sample of size 1 is to be taken froma finite population of size $N$a. How many possible samples are there?b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration.c. What is the difference between taking a random sample of size 1 from a population and selecting a member at random from the population?
Step 1
Given that the population size is $N$, the number of possible samples is equal to the number of elements in the population. Therefore, there are $N$ possible samples. Show more…
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Suppose that a random sample of size 1 is to be taken from a finite population of size N. Answer parts (a) through (c) below. a. How many possible samples are there? A. 1 B. N - 1 C. N D. N + 1 b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration. Choose the correct answer below. A. At least one sample mean is equal to the population mean, or the mean of all possible observations. B. Each possible sample mean is equal to an observation, only if the population is normally distributed. C. Each possible sample mean is equal to an observation, regardless of the nature of the population. D. Since the samples are of size 1, there is 1 possible sample mean, and it is equal to the sample mean. c. What is the difference between taking a random sample of size 1 from a population and selecting a member at random from the population? A. There is no difference because there is only one possible sample when the population is size 1. B. The distribution of the sample mean for samples of size 1 has a larger standard deviation than that of the population. C. There is no difference because the sample includes just one random member from the population. D. The distribution of the sample mean for samples of size 1 has a smaller standard deviation than that of the population.
Suppose that a random sample of size 1 is to be taken from a finite population of size N. Answer parts (a) through (c) below. a. How many possible samples are there? A. N B. N+1 C. N-1 D. 1 b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration. Choose the correct answer below. A. Each possible sample mean is equal to an observation, only if the population is normally distributed. B. Each possible sample mean is equal to an observation, regardless of the nature of the population. C. At least one sample mean is equal to the population mean, or the mean of all possible observations. D. Since the samples are of size 1, there is 1 possible sample mean, and it is equal to the sample mean. c. What is the difference between taking a random sample of size 1 from a population and selecting a member at random from the population? A. The distribution of the sample mean for samples of size 1 has a larger standard deviation than that of the population. B. There is no difference because the sample includes just one random member from the population. C. There is no difference because there is only one possible sample when the population is size 1. D. The distribution of the sample mean for samples of size 1 has a smaller standard deviation than that of the population.
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