Statistics Notes Chapter 5 Of Agresti And Finlay

Front 1

Define what a point estimator (estimate)is, and list two qualities that a good point estimator should have.

Back 1

A Point estimator (estimate) is a sample statistic that predicts the value of the parameter. A good point estimator should unbiased (centred around parameter) and efficient (low standard error).

Front 2

Explain what a "biased" estimator is and give an example.

Back 2

A biased estimator is one that, on the average, consistently over or under estimates the population parameter. Eg: in an uneven distribution, using the sample median as the estimate would be biased since the mean is skewed.

Front 3

True or false - the concept of bias refers only to one sample, not to the estimator's behaviour in repeated samples.

Back 3

False - the concept of bias in this instance refers to the estimator's behaviour in repeated samples - not just one.

Front 4

Why is an efficient estimator preferable?

Back 4

An efficient estimator, one that has as low of a standard error as possible, is preferable since, on the average, it falls closer than the other estimators to the parameter.

Front 5

What is the definition AF provide for an interval estimate?

Back 5

An interval estimate is a range of numbers around the point estimate, within which the parameter is believed to fall.

Front 6

A survey taken in May 1996 reported that 55% of the American public approved of President Clinton's performance in office. Is this an example of a point estimate or of the parameter?

Back 6

This survey is an example of a point estimate, not the parameter. Point estimates are the most common form of inference used by the mass media.

Front 7

R.A. Fisher made many important contributions to statistics, including a method for point estimators. What is that method calle?

Back 7

"Maximum likelihood estimate"

Front 8

What is the "Maximum Likelihood estimate"?

Back 8

The value of the parameter that is most consistent with the observed data in that if the parameter equaled a certain number (say 44), then the observed data has a greater chance of being 44 than any other number.

Front 9

Fisher showed that, for large samples, maximum likelihood estimates have three properties. List them.

Back 9

1. They are efficient.
2. They have little, if any bias.
3. They are approximately normal distributions.

Front 10

in order for an inference to be informative it must do two things. What are they?

Back 10

- provide an inference about the paramter.
- indicate how accurate it is.

Front 11

Give an example of how the point estimator depends on the characteristics of the sampling distribution.

Back 11

- If it is a normal distribution, than there is a high (.95) probability that the estimator falls within 2 standard deviations of the parameter. The smaller the standard error the more accurate the estimator tends to be.

Front 12

Define confidence interval and confidence coefficient.

Back 12

- Confidence interval is a range of numbers within which the parameter is believed to fall.
- Confidence Coefficient is the probability that the range includes the parameter. It is close to 1, such as .95 or .99.

Front 13

What does the Central Limit Theorem state?

Back 13

That for large random samples, the sampling distribution of the mean is approximately normal.

Front 14

For populations over 30, what is a good substitute for the unknown standard error?

Back 14

A good replacement for the standard error formula is the formula s over the square root of n (s/n).

Front 15

What are the formulas for a 95 and 99 % confidence interval?

Back 15

Y +- 1.96(s)
Y +- 2.58 (s)

Front 16

What does the error in the confidence interval refer to? List some other reasons for error.

Back 16

It only refers to the sampling error. Other reasons for error include non-response (refusing to answer) or measurement error (when a respondent lies).

Front 17

Why wouldn't a 100% Confidence Interval be employed?

Back 17

It is not informative. It includes all numbers from 0- infinity, so it really doesn't tell us ANYTHING. Use 99% if you must, or 95%, but not 100.

Front 18

What do you gain by using a 99% confidence interval, and what do you sacrifice?

Back 18

- You gain more assurance that it contains the parameter, but you lose presicion.

Front 19

Explain how you'd find out a 98% confidence interval.

Back 19

1. You know that the confidence coefficient would be 1-.98=.02
2. .02 would be in both tails, so you'd divide it in 2. .02/2, which gives .01 in each tail.
3. Look up .01 in table A (that's your z-score)

Front 20

What is one way that a researcher can improve the precision of a confidence interval?

Back 20

By increasing the sample size

Front 21

In order to double the precision, what must one do to the sample size?

Back 21

Quadruple it. Quadruple the sample size to double the precision.

Front 22

Give one reason why the width of the confidence interval would:
1) Increase
2) Decrease

Back 22

The confidence interval would
1. Increase as the confidence coefficient (1-.99) increases
2. Decrease as the sample size increases.

Front 23

List the two things that influence the size of the sample you need.

Back 23

1. Precision
2. Probability

Front 24

What sort of sampling types do the sample size formulas given in the text book refer to?

Back 24

- They are good for a) Simple random sampling and
b) for systematic random sampling

Front 25

What is the formula given to estimate the sample size needed for a mean?

Back 25

N= sxs (standard dev. squared) x (z/B)squared (z/b)x(z/b).

Front 26

Would you need a larger sample size for a homogeneous or heterogeneous population?

Back 26

You'd need a larger sample size for a heterogeneous population.

Front 27

List five considerations in determining sample size

Back 27

1. Precision
2. confidence
3. variability (in population)
4. The complexity of analysis
5. Resources (time, money etc)