Exam 7: Sampling and Sampling Distributions

The standard deviation of is usually called the

The Central Limit Theorem (CLT)states that the sampling distribution of the mean is approximately normal,no matter what the distribution of the population,so long as the sample size is large enough.

(A)What sample size would be required for the production personnel to be approximately 95% sure that their estimate of the average number of defective batteries per box is within 0.3 unit of the true mean? Assume that the best estimate of the population standard deviation ( )is 0.9 defective batteries per box. (B)How does your answer to (A)change if the production personnel want their estimate to be within 0.5 unit of the actual population mean? Evaluate the tradeoff between required accuracy and sample size requirement for this case and the case in (A).

Estimation is the process of inferring the value of an unknown population parameter using data from a random sample

In sampling,a population is:

When we sample less than 5% of the population,the finite population correction factor; fpc = ,is used to modify the formula for the standard error of the sample mean.

(A)Suppose that Sally wishes to examine a representative subset of these 60 houses that has been stratified by the number of bedrooms.Use Excel to assist her by finding such a stratified sample of size 10 with proportional sample sizes. (B)Explain how Sally could apply cluster sampling in selecting a sample of size 15 from this frame. (C)What are the advantages and disadvantages of employing cluster sampling in this case?

One obvious advantage of stratified sampling is that we obtain separate estimates within each stratum - which we would not obtain if we took a simple random sample from the entire population.A more important advantage is that we can increase the accuracy of the resulting population estimates by using appropriately defined strata.

The key to using stratified sampling is:

The standard error of sample mean is large when the observations in the population are spread out (large ),but that the standard error can be reduced by taking a smaller sample.

A sample chosen in such a way that every possible subset of same size has an equal chance of being selected is called a(n)

The standard error of an estimate is the standard deviation of the sampling distribution of the estimate.It measures how much estimates from different samples vary.

With proportional sample sizes:

The randomized response technique is a way of getting at sensitive information to avoid estimation errors due to nontruthful responses.

We can measure the accuracy of judgmental samples by applying some simple rules of probability.This way,judgmental samples are not likely to contain our built-in biases.

Which of the following are reasons for why simple random sampling is used infrequently in real applications?

An estimator is said to be unbiased if the mean of its sampling distribution equals the value of the population parameter being estimated.

If systematic sampling is chosen as the sampling technique,it is probably because:

The defining property of a simple random sample is that:

The sampling distribution of the mean will have the same standard deviation as the original population from which the samples were drawn.