Exam 10: Sampling and Sampling Distributions

The possible presence of hidden periodicities is a danger of _______ sampling.

The variance of the sampling distribution can be equal to the variance of the population.

A random sample of size 36 is selected from a population of size 101 whose standard deviation is 5 . The standard error of the mean is _______.

The mean number of errors in a random sample of 100 accounts to be audited is used to estimate the mean of the population of accounts having a standard deviation of $\sigma=4$ . What is the probability that the error will be less than 0.8 -using the central limit theorem?

If we want to change a standard error from 12 to 4 by changing the sample size, we need to multiply the original sample size by

It is impossible to apply the central limit theorem if the population does not follow a normal distribution.

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining. -In how many ways can the investor select two stocks to buy?

A simple random sample from a finite population is a sample which is chosen in such a way that each possible sample has the same probability of being selected.

Sampling with replacement from a finite population is, in effect, sampling from an infinite population.

An important goal of _______ sampling is that there is less variability within the resulting subgroups than in the entire population.

Random samples of size 2 are selected from the finite population which consists of the numbers 4, 7, 10, 13, 16, and 19. -List the 15 possible random samples of size 2 that can be selected from the finite population, and calculate their means.

The central limit theorem applies in situations when $n$ constitutes a large proportion of the population.

A stratified sample is taken from a population of size $N=2000$ which consists of two strata of $N_{1}=800$ , $N_{2}=1200, n_{1}=20, n_{2}=40, \sigma_{1}=3, \sigma_{2}=5$ . Then the method of allocation is

The mean of a random sample of size 49 is used to estimate the mean of a very large population, consisting of the lifetimes of certain stereo components which have a standard deviation of $\sigma=35$ hours. What is the probability that our estimate will be in error by -less than 8 hours?

In order for $\sigma_{\bar{\chi}}^{\bar{x}}$ to be as low as possible in stratified sampling, it is preferable that each of the strata have as little homogeneity as possible.

A sampling distribution of the mean is always a probability distribution whose values are sample means.

A stratified sample of size $n=300$ is to be taken from a population of size $N=30,000$ which consists of four strata for which $N_{1}=10,000, N_{2}=5,000, N_{3}=8,000, N_{4}=7,000, \sigma_{1}=15, \sigma_{2}=25, \sigma_{3}=20$ and $\sigma_{4}=30$ . How large a sample must be taken from each stratum if the allocation is to be -optimum?

Suppose that in a group of six athletes there are three jockeys whose heights are 60,65 , and 55 inches, and three basketball players whose heights are 80,75 , and 85 inches. -Suppose that the six athletes are divided into clusters according to their sports, each cluster is assigned a probability of $\frac{1}{2}$ , and a random sample of size 2 is taken from one of the randomly chosen clusters. List all possible samples, calculate their means, and calculate $\sigma_{\bar{x}}$ .

Using the population of the numbers $10,38,25,18,42,15$ , construct the sampling distribution of the median for random samples of size $n=3$ drawn without replacement from the given population.

Suppose that in a group of six athletes there are three jockeys whose heights are 60,65 , and 55 inches, and three basketball players whose heights are 80,75 , and 85 inches. -List all possible random samples of size 2 which may be taken from this population. Calculate the means of these samples, and calculate $\sigma_{\bar{x}}$ .