Statistics Unplugged

Family of t distributions

a series of sampling distributions developed by Gossett. The shape of any one distribution is a function of sample size.

What Z value is associated with a 95% confidence interval? What Z value is associated with a 99% confidence interval?

A Z value of 1.96 is used for a 95% confidence interval. A Z value of 2.58 is used for a 99% confidence interval.

Given a constant level of confidence, what is the effect on the margin of error of increasing the sample size?

An increase in the size of a sample will decrease the margin of error.

what is a confidence interval for the mean?

An interval or range of values withing which the true mean of the population is believed to be located.

What is the purpose behind the construction of a confidence interval for a proportion?

Confidence interval for a proportion is constructed in an effort to estimate the proportion in a population, based upon proportion in a sample.

What effect does increasing the size of a sample have on the width of the confidence interval and the precision of the estimate?

Decreases the width of the interval and, therefore, increases the precision of the estimate.

When constructing a confidence interval for the mean, how do you approach the standard error? How does the approach differ, depending on whether you know the value of the standard deviation of the population?

If the population is known, you make a direct calculation of the value of the standard error. If population is unknown, you have to estimate the value of the standard error.

Assume that you are going to construct a confidence interval for the proportion using a 99% level of confidence. If you increased your sample size, what would happen to the width of the interval?

It would decrease

what is the relationship between the level of confidence and precision of an estimate when constructing a confidence interval for the mean?

Level of confidence and precision are inversely related. As one increases, the other decreases.

When using the t table and constructing a confidence interval for the mean (with population unknown), how do you find the level of confidence in the table?

Level of confidence is expressed indirectly. It is equal to 1 minus the level of significance.

How is the standard error calculated when the standard deviation of the population is known?

Standard deviation of the population is divided by the square root of the sample size.

What is the relationship between the standard deviation of the population and the standard error (the standard deviation of the sampling distribution of sample means)?

Standard error is equal to population divided by the square root of the sample size.

how is a confidence interval for the mean constructed?

Sample mean is used as the starting point. A value is added to the mean and subtracted from the mean. The results are the upper and lower limits of the interval.

In a confidence interval for a proportion, what is the margin of error?

The margin of error is an indirect statement of the width of the interval.

When using the t table and constructing a confidence interval for the mean (with population unknown), how is the number of degrees of freedom computed?

The number of degrees of freedom will equal n-1 (the size of the sample, minus 1)

How do you estimate the value of the standard error of the mean (s x bar)?

The standard error of the mean is estimated by dividing the sample standard deviation (s) by the square root of the sample size.

When constructing a confidence interval for the mean with sigma unknown, the standard error of the mean is derived by:

dividing s by the square root of n

When using Appendix B in your text (Family of t Distributions) to construct a confidence interval for the mean, how are degrees of freedom calculated?

n-1