Chapters 8 and 9 (book) stats

Confidence interval

A confidence interval is a range of values within which the population parameter is expected to occur.

Cluster sampling

A method often used to lower the cost of sampling if the population is dispersed over a wide geographic area. The area is divided into smaller units called primary units. Then a few primary untis are chosen, and a ra

Stratified random sampling

A population is first divided into subgroups called strata.

Bias

A possible consequence if certain members of the population are denied the chance to be selected for the sample. As a result, the sample may not representative of the population.

Sampling distribution of the sample mean

A probability distribution consisting of all possible means of samples of a given size selected from the population.

What is a proportion in terms of estimation and confidence intervals?

A proportion is a ratio, fraction, or percent that indicats the part of the sample or population that has a particular characteristic.

Probability sample

A sample of items or individuals chosen so that each member of the population has a chance of being included in the sample.

How is a sample proportion found?

A sample proportion is found by X, the number of successes, divided by n, the number of observations.

Simple random sampling

A sampling scheme such that each member of the population has the same chance of being selected as part of the sample.

Point estimate

Asingle value computed from a sample and used to estimate a population parameter. Example: if the sample mean is 1020, it is the best estimate of the population mean.

Systematic random sampling

Assuming the population is arranged in some way, such as alphabetically, by height, or in a file drawer, a random starting point is selected, then every kth item becomes a member of the sample.

What is the relationship between the sample and population means?

For a given sample size, the mean of all possible sample means selected from a population is equal to the population mean.

For a finite population, how is the standard error adjusted?

It is adjusted by the factor:

Sampling error

The difference between a population parameter and a sample statistic.

Sampling error

The difference between a sample statistic and the corresponding population parameter.

Interval estimate

The interval within which a population parameter probably lies, based on sample information. Example: According to sample data, the population mean is in the interval between 1.9 and 2.0 pounds.

What is a sampling distribution?

The sampling distribution of the sample mean is a probability distribution of all possible sample means of the sample size.

Central limit theorem

The sampling distribution of the sample mean will approach a normal distribution regardless of the shape of the population as sample size increases.

How is the standard error found?

The standard error of the mean measures the variation in the sampling distribution of the sample mean. The standard error is found by:

How does variation in the distribution of the sample mean differ from variation in the distribution of the population mean?

There is less variation in the distribution of the sample mean than in the population distribution.

To determine the confidence limits when the population standard deviation is unknown

We use the t distribution

How to determine the level of confidence when the population standard deviation is known

We use the z distribution

Finite-population correction factor (FPC)

When sampling without replacement from a finite population, a correction term is used to reduce the standard error of the mean according t othe relative size of the sample to the size of the population. The correction factor is used when the sample is more than 5 percent of the finite population.

The major characteristics of the t distribution are

1. It is a continuous distribution 2. It is mound-shaped and symmetrical 3. It is flatter, or more spread out, than the standard normal distribution. 4. There is a family of t distributions, depending on te number of degrees of freedom.

What are the three factors that determine the sample size when we wish to estimate a proportion?

1. The margin of error, E. 2. The desired level of confidence. 3. A value for probability to calculate the variation in the population.

What are the three factors that determine the sample size when we wish to establish the mean?

1. The margin of error, E. 2. The desired level of confidence. 3. The variation in the population.

Factors that determine the width of a confidence interval for a mean are:

1. The number of observations in a sample, n 2. The variability in the population, usually estimated by the sample standard deviation, s. 3. The level of confidence