Statistics Chapter 5 & 6

Front 1

If repeated random samples of size n are taken from a population with a mean (µ) and a standard deviation (σ), the sampling distribution of sample means will have a mean equal to µ and a standard error equal to σ/√n

Back 1

Central Limit Theorem

Front 2

As n increases the sampling distribution will approach a normal distribution.

Back 2

Central Limit Theorem

Front 3

A physical representation of the population; a listing of all the elements in a population.

Back 3

Sampling Frame

Front 4

The standard deviation of a sampling distribution of sample means.

Back 4

Standard Error of the Mean

Front 5

The result that you would get if you took repeated samples from a given population, calculated from the mean for each sample, and plotted the sample means.

Back 5

Sampling Distribution of Sampling Means

Front 6

The difference between a sample statistic and a population parameter that is due to chance.

Back 6

Sampling Error

Front 7

A sample selected in a way that every unit has an equal chance of being selected, and the selection of any one unit in no way affects the selection of any other unit.

Back 7

Random Sample

Front 8

In a random sample, every unit in the population has an_____chance of being selected.

Back 8

equal

Front 9

In a random sample, does the selection of any one unit affect the selection of another unit?

Back 9

No.

Front 10

In a random sample, how many combinations are possible?

Back 10

ALL.

Front 11

When selecting a sample, the physical representation of the population is known as the______?

Back 11

Sampling Frame

Front 12

The difference between a sample statistic and population parameter that is due to chance is referred to as_____?

Back 12

Sampling Error

Front 13

A sampling distribution of sample means is based on taking repeated samples (of size n) from the same population and plotting the_______ of different samples.

Back 13

Means

Front 14

According to Central Limit Theorem, the mean of a sampling distribution of sample means will equal the _____ of the population from which the samples were drawn.

Back 14

Mean

Front 15

The standard deviation of a sampling distribution of sample means is referred to as the______ _______ of the _____.

Back 15

Standard Error of the Mean

Front 16

According to the Central Limit Theorem, and given a sampling distribution of sample means, the standard error of the mean will equal the _____ ______ of the population divided by the square root of the sample size.

Back 16

Standard Deviation

Front 17

According to the Central Limit Theorem, and given a sampling distribution of sample means, the standard error of the mean will equal the standard deviation of the population divided by the ____ ____ of the sample size.

Back 17

Square Root

Front 18

The shape of a sampling distribution of sample means will approach the shape of what kind of curve?

Back 18

Normal.

Front 19

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

Back 19

Confidence Interval for the Mean

Front 20

A statement of two values (or an interval) within which you believe the true proportion of the population is found.

Back 20

Confidence Interval for a Proportion

Front 21

An estimate of the standard deviation of the sampling distribution of sample means; a function of the standard deviation of a sample.

Back 21

Estimate of the Standard Error of the Mean

Front 22

A series of sampling distributions (of the t statistic) developed by Gossett. The shape of any one distribution is a function of sample size (or degrees of freedom, equal to n-1).

Back 22

Family of t distributions

Front 23

The amount of confidence that can be placed in an estimate derived from the construction of a confidence interval. Level of confidence is mathematically defined as 1 minus the level of significance. The level of confidence is a statement of percentage of times (99%, 95%, etc.) one would obtain a correct confidence intervals if one repeatedly constructed confidence intervals for repeated samples from the same population.

Back 23

Level of confidence

Front 24

A term used to express the width of a confidence interval for a proportion.

Back 24

Margin of Error

Front 25

How is a confidence interval for the mean constructed?

Back 25

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

Front 26

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

Back 26

1.96

Front 27

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

Back 27

2.58

Front 28

What is the relationship between the LEVEL OF CONFIDENCE and the PRECISION OF AN ESTIMATE when constructing a confidence interval for the mean?

Back 28

Level of confidence and precision are inversely related. AS ONE INCREASES, THE OTHER DECREASES.

Front 29

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

Back 29

it DECREASES THE WIDTH of the interval and, therefore, INCREASES THE PRECISION of the estimate.

Front 30

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 (σ)?

Back 30

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

Front 31

How do you estimate the value of the standard error of the mean (sXbar)?

Back 31

by dividing the sample standard deviation (s) by the square root of the sample size (√n).

Front 32

how is the degrees of freedom computed?

Back 32

n-1 (size of sample - 1).

Front 33

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

Back 33

The level of confidence is expressed indirectly. It is equal to 1 minus the level of significance. For example, to work at the 95% level of confidence, use the column dedicated to the .05 level of significance (1 - .05 = .95).

Front 34

A statement of two values (or an interval) within which you believe the true mean of the population (µ) is found.

Back 34

Confidence interval for the mean

Front 35

An estimate of the standard deviation of the sampling distribution of sample means; a function of the standard deviation of a sample.

Back 35

estimate of the standard error of the mean

Front 36

A series of sampling distributions (of the t statistic) developed by Gossett. The shape of any one distribution is a function of sample size (or degrees of freedom, equal to n - 1).

Back 36

family of t distributions

Front 37

The amount of confidence that can be placed in an estimate derived from the construction of a confidence interval. Level of confidence is mathematically defined as 1 minus the the level of significance. The level of confidence is a statement of the percentage of times (95%, 99%, etc) one would obtain a correct confidence interval if one repeatedly constructed confidence intervals for repeated samples from the same population.

Back 37

level of confidence

Front 38

A term used to express the width of a confidence interval for a proportion.

Back 38

Margin of Error