Exam 8: Sampling Methods and the Central Limit Theorem

We can expect some difference between sample statistics and the corresponding population parameters.This difference is called the sampling error.

What is the difference between a sample mean and the population mean called?

A sampling distribution of the means is a probability distribution consisting of a list of all possible sample means of a given sample size selected from a population and the probability of occurrence associated with each sample mean.

The mean weight of trucks traveling on a particular section of I-475 is not known.A state highway inspector needs an estimate of the mean.He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons,with a standard deviation of the sample of 4.2 tons.What is probability that a truck will weigh less than 14.3 tons?

The Central Limit Theorem states that for a sufficiently large sample the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to $\sigma$ ²and the variance equal to $\sigma$ ^2/n.

As the sample size (n)increases,what happens to the spread or dispersion of the distribution of the sample means? ___________

What is a characteristic of a population called? _______________

Based on the sampling distribution of the means and the central limit theorem,the sample mean can be used as a good estimator of the population mean,assuming that the size of the sample is sufficiently large.

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.For a set of four tires,what is the probability that the average tire life is between 57,000 and 63,000 miles?

When dividing a population into subgroups so that a random sample from each subgroup can be collected,what type of sampling is used?

An accounting firm is planning for the next tax preparation season.From last year's returns,the firm collects a systematic random sample of 100 filings.The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.What is the probability that the mean completion time is between 1 and 2 hours,i.e. ,60 and 120 minutes?

Based on the central limit theorem,the mean of all the sample means is

In cluster sampling,a population is divided into subgroups called clusters and a sample is randomly selected from each cluster.

Which sampling method would you use if every k-th item in the population sequence is selected? ______________________

All possible samples of size n are selected from a population and the mean of each sample is determined.What is the mean of the sample means?

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spend studying per week.Based on a simple random sample,they surveyed 144 students.The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours.What is the standard error of the mean?

The Central Limit Theorem states that if the sample size,n,is sufficiently large,the sampling distribution of the means will be approximately normal no matter whether the population is normally distributed,skewed,or uniform.

In cluster sampling,a population is divided into clusters using naturally occurring geographic or other boundaries.Then clusters are randomly selected and a random sample is collected from each cluster.

If the sample size equals the population size,what is the sampling error? _________

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires.The average tread wear was found to be 50,000 miles with a standard deviation of 3,500 miles.What is the best estimate of the average tread life in miles for the entire population of these tires?