Qm - Module 8 - Statistical Inference

Front 1

Define Statistical Inference

Back 1

Set of methods by which data from samples can be turned into more general information about populations.

Front 2

What are two main parts of Statistical Inference?

Back 2

1. Estimation - making predictions and specifying their accuracy.
2. Significance Testing - distinquishing between a result arising from chance and one arising from other factors.

Front 3

How is Statistical Inference used to prove or disprove a hypothesis?

Back 3

Through significance testing

Front 4

Describe estimation

Back 4

a form of inference where a sample is the basis for predicting the values of population parameters.

Front 5

What are several key applications of Statistical Inference

Back 5

1 Market research
2. Medicine - significance testing helps to decide whether treatments are beneficial

Front 6

Describe Confidence level

Back 6

To allow for possibility that conclusions drawn from the sample may be wrong due to the sample not being representative, the confidence level is a statement of probability that the statement is true.

Front 7

What helps to make inference easier and more accurate?

Back 7

Sampling Distribution of the Mean

Front 8

Describe the Sampling Distribution of the Mean

Back 8

The mean of a series of samples chosen at random. This mean has a distribution.

Front 9

What are the characteristics of the Sampling Distribution of the Mean?

Back 9

a. Shape - normal distribution
b. Mean - same as the individual distribution from which samples taken
c. Standard Deviation - if s is the SD from the individual distribution, then the SD for this distribution is s divided by the square root of the sampling size.

Front 10

Why is using at least 30 as sample important in working with the Sampling Distribution?

Back 10

a. The shape of the sampling distribution will be normal regardless of original distribution.
b. The standard deviation of the sampling distribution will be the same as the population standard deviation.

Front 11

What does the Central Limit Theorem say?

Back 11

As the sample size increases, the sampling distribution of the mean becomes progressively more normal.

Front 12

The mean of the sample is known as ...

Back 12

the point estimate of the population mean.

Front 13

The Range for the population mean is stated as

Back 13

the range 00 - 00 is the 95 percent confidence limits.

Front 14

The notation for population measures are written using ...

Back 14

Greek letters

mu (myoo) is used for arithmetic mean of the population

sigma is used for standard deviation of the population

Front 15

List general procedure for estimating the mean of a population

Back 15

1. Take a random sample of at least 30
2. Calculate sample mean and standard deviation.
3.Standard deviation of sampling distribution of the mean (standard error) is s divided by the square root of the number in the sample.
4. Point estimate of the population is the mean.
5. 95 percent confidence limits for the population mean are the mean +/- 2s x the square root of the sample size.

Front 16

What are the steps for Basic Significance test methodology?

Back 16

1. Formulate the hypothesis
2. Collect a sample of evidence
3. Decide on significance factor
4. Calculate the probability of the sample evidence occurring.
5. Compare the probability with the significance level.

Front 17

What is the null hypothesis?

Back 17

The statistical hypothesis that states that there are no differences between observed and expected data. In science, the null hypothesis has traditionally been something the experimenter is trying to disprove.

Front 18

What is the alternative hypothesis?

Back 18

What we conclude if the null hypothesis is disproved.

Front 19

When the hypothesis is rejected, the result is said ...

Back 19

to be significant at the 5% level.

Front 20

What is alternative procedure to Significance level testing?

Back 20

Comparison of the Observed sample mean with the Critical Value.

Front 21

Define Critical Value

Back 21

the value of the sample mean lying exactly on the boundary separating significant from non-significant results.

Front 22

Define one-tailed test

Back 22

checking the hypothesis at one tail of the distribution

Front 23

Define two-tailed test

Back 23

checking the hypothesis at both tails of the distribution

Front 24

Describe a type 1 error

Back 24

when a hypothesis is true but a sample statistic in a reject tail of the distribution occurs and the hypothesis is falsely rejected.

Front 25

Describe a Type 2 error

Back 25

a mistake that causes the hypothesis to be accepted when it is false.

Front 26

The power of the significance test is ...

Back 26

the probability of correctly accepting the alternative hypothesis.

Front 27

If the null hypothesis is true

Back 27

P(correctly accepting null hypothesis) = 95%
P(erroneously rejecting null hypothesis) = 5% (Type 1 error)

Front 28

If the alternative hypothesis is true

Back 28

P(correctly accepting alternative hypothesis) is the power of the test
P(erroneously rejecting alternative hypothesis) = 100% - power (type 2 error)

Front 29

A significance test is directly comparable to ...

Back 29

the estimation of confidence levels.

Front 30

For a 2-tailed test, the rejection of a hypothesis at the 5% level from sample data is the same as ...

Back 30

the hypothesized mean not falling within the 95% confidence interval of the population mean.

Front 31

For a 2-tailed test, the acceptance of a hypothesis at the 5% level from sample data is the same as ...

Back 31

the hypothesized mean falling within the 95% confidence interval of the population mean estimated from the same same

Front 32

For a one-tailed test, the rejection of a hypothesis at the 5% level from sample data is the same as ...

Back 32

the hypothesized mean not falling within the 90% confidence interval of the population mean estimated from the same mean.

Front 33

For a one-tailed test, the acceptance of a hypothesis at the 5% level from sample data is the same as ...

Back 33

the hypothesized mean falling within the 90% confidence interval of the population mean estimated from the same sample.

Front 34

How is significance test performed when there are two samples?

Back 34

The significance test is based on a distribution based on the difference in sample means of the two samples.

Front 35

The mean of a distribution of the difference in sample means equals?

Back 35

Zero

Front 36

Describe the Variance Sum Theorem

Back 36

if x and y are two variables, then the variance of their sum or difference is:

Var(x + y) = Var(x) + Var(y)
Var(x - y) = Var(x) + Var(y)

Front 37

Describe the procedure for comparing the difference between paired samples.

Back 37

1. Form a single new sample which is the differences between the observations taken in pairs.
2. New sample treated as for basic single sample significance test.