Exam 2: Glossary

Question 1

14 What is the sampling distribution of x-bar a distribution of?

Hint: what is x-bar?

Answer 1

Distribution of the sample mean; a list of all the possible values for x together with the frequency (or probability) of each value

Question 2

15 Define the Central Limit Theorem (CTL)

Answer 2

When n > 30 the sample distribution will be a normal curve despite the shape of the original population (right-skewed, left-skewed, etc)

The name of the theorem stating that the sampling distribution of a statistic (e.g. x​ ̄) is approximately normal whenever the sample is large and random

Question 3

15 Define the Population Distribution

Answer 3

The distribution of all the observations in a population

Question 4

15 Define standard deviation of sampling distribution of x-bar

Answer 4

The standard deviation of the population divided by the sort of sample size
σ/sqrt(n)

A measure of the variability of the sampling distribution of x​ ̄; the “average” amount that the statistic, x​ ̄, deviates from its associated parameter, μ; equals σ / sqrt(n)

Question 5

15 Define mean of sampling distribution of x-bar

• not in glossary

Answer 5

mean of sampling distribution of x-bar is equal to the population mean

mean x-bar = population mean

Question 6

15 What is the shape of sampling distribution of x-bar?

• not in glossary

Answer 6

Bell-shape, the normal distribution

Question 7

15 Define Simple Random Sample

Answer 7

A sample of size n selected from the population in such a way that each possible sample of size n has an equal chance of being selected

Question 8

16 Define Statistical Process Control (SPC)

Answer 8

A quality control method which uses statistics (info about samples) to monitor and control a process

A procedure used to check a process at regular intervals to detect problems and correct them before they become serious

Efficiency Check
Standardization of products

Tools: Control Charts

Question 9

16 Control chart

Answer 9

A chart plotting the means ( x​ ̄’s) of regular samples of size n against time. It has a center line and upper and lower control limits to determine whether a process is in control or out of control. (A chart to monitor the values of the inputs and outputs of a process)

Question 10

Control Limits

Answer 10

Upper and lower bounds of natural variability

Lines on either side of the center line computed
using A sample mean outside of these bounds signals that the process is out of control

mu-(3 * ( sd/sqrt(n) ) )

Question 11

Natural Variation

Answer 11

Variation from object to object within a population

Question 12

16 Out-of-control signals

Answer 12

One sample mean outside the control limits (three standard deviations
from ​x̄)

or

nine sample means in a row above (or below) the center line in a control chart

Question 13

Process

*not in glossary

Answer 13

Series of steps/instructions to produce something

Question 14

16 Process control

*not in glossary

Answer 14

Quality of the process so we get the outcome we want

Question 15

16 Target value

Answer 15

The desired mean of a process that is in control

Question 16

16 Unnatural variation

Answer 16

Variation from outside factors from an object, special cases

Question 17

16 x-bar chart

Answer 17

A specfic type of control chart containing mean x-bars

Question 18

17 Statistical Inference

*not in glossary

Answer 18

The process of inferring something about the population base on what is measured in the sample

Question 19

17 Statistic vs. Parameter

Answer 19

Statistic - value of the sample

Parameter - value about the population

Question 20

17 Point estimation

*not in glossary

Answer 20

Estimate an unknown parameter with a SINGLE number calculated from the sample data

• Ex: Based on the sample, we estimate that p, the proportion of all U.S. adults who are in favor of stricter gun control, is 0.6.
• 0.6 = single number

if quantitative = population mean μ

if categorical = Proportion (p)

Question 21

17 Interval estimation

*not in glossary

Answer 21

Estimate an unknown parameter with an interval of values that will likely include the actual parameter value

• Ex: Based on the sample, we are 95% confident that p, the proportion of U.S. adults who are in favor of stricter gun control, is between 0.57 and 0.63.
• 0.57 and 0.63 = interval

Question 22

17 Hypothesis testing

*not in glossary

Answer 22

Statistical hypothesis testing is defined as:

Assessing evidence provided by the data in favor of or against some claim about the population.

Make a prediction/claim about the population. Then check if the sample data provides evidence to support that.

• Ex: It was claimed that among all U.S. adults, about half are in favor of stricter gun control and about half are against it. In a recent poll of a random sample of 1,200 U.S. adults, 60% were in favor of stricter gun control. This data, therefore, provides some evidence against the claim.
• “claim” is the keyword

Question 23

17 Estimator

*not in glossary

Answer 23

A general statistic that estimates the parameter

Ex: the x-bar sample mean is an estimator for the population mean μ

Question 24

17 Estimate

Answer 24

A specfic value of an estimator

Ex: If the estimator x-bar is 5 the estimate is the value 5

Question 25

17 Unbiased estimator

Answer 25

A condition where the mean of all possible statistics equals the parameter that the statistic estimates

• Random sample

Note: As size n increases accuracy increases

Question 26

18 Estimate of a parameter

Answer 26

A single value or a range of values used to estimate a parameter

Question 27

18 Confidence Interval

Answer 27

An estimate of the value of a parameter in interval form with an associated level of confidence; it gives a list of plausible values for the parameter based on the value of the statistic

An estimate of a parameter value in interval form with a level of confidence (percent of values within a range)

The interval has possible values for the parameter

Question 28

18 Confidence Level

Answer 28

The percentage of all possible samples for which the confidence intervals will contain the parameter being estimated; selected subjectively by the researcher

Question 29

19 Difference between variable and parameter

Answer 29

variable - What is actually being measured on each subject

parameter - Overview of the data, summarizes the variable, about population

Question 30

20 P-value

Answer 30

P-value: Probability of getting a test statistic as extreme of more extreme than observed if H0 were true

Question 31

20 Alternative Hypothesis

Answer 31

Alternative hypothesis: A statement about the value of a parameter that is either “less than”, “greater than”, or “not equal to” a hypothesized number or another parameter; the hypothesis that the researcher usually wants to prove or verify

Question 32

20 Claimed parameter value

Answer 32

Claimed parameter value: The value of the parameter as given in the null hypothesis

Question 33

20 Null Hypothesis

Answer 33

Null hypothesis: The hypothesis that the researcher assumes to be true until sample results indicate otherwise; the hypothesis of no difference or no change; usually the hypothesis that the researcher wants to disprove

Question 34

20 Level of significance/significance level (alpha)

Answer 34

Level of significance/significance level (alpha): Probability of Type 1 error, i.e probability of rejecting a true null hypothesis; the largest risk of rejecting a true null hypothesis that a researcher is willing to take

Question 35

20 Statistical significance

Answer 35

If something is statistically significant the difference between the observed statistic and the claimed parameter value as given in H0 is too large to be due to chance alone.

To assess, ask “Is P-value < alpha?” if yes, then results are statistically significant. (Too unusual)

Question 36

20 Test statistic

Answer 36

Test statistic: A numerical value calculated from the sample information assuming H0 is true; used to obtain P-value. (ex: x-bar)

Question 37

20 Test of significance

Answer 37

Test of significance/test of hypothesis: A statistical procedure for making decisions about parameter values based on probabilities of the associated statistic(s)

(x-bar - μ) / (s/sqrt(n))

Question 38

21 - 4 step process

*not in the glossary

Answer 38

4 step process: STATE, PLAN, SOLVE, CONCLUDE

Question 39

21 Sample standard deviation

Answer 39

Sample standard deviation: A measure of the variability of data in a sample about x-bar

Question 40

21 Student’s t distribution

Answer 40

Student’s t distribution: A distribution specified by degrees of freedom used to model test statistics for the sample mean, differences between sample means, etc. where IT(’s) is/are known

Question 40

21 Student’s t distribution

Answer 40

Student’s t distribution: A distribution specified by degrees of freedom used to model test statistics for the sample mean, differences between sample means, etc. where IT(’s) is/are known

Question 41

21 t*

*not in glossary

Answer 41

t*: The t-statistic?

Question 42

21 t test

Answer 42

Any significance test where the test statistic can be modeled with the t-distribution (used when σ is unknown)

Question 43

22 Observed effect

Answer 43

Observed effect: The difference between a statistic and claimed/hypothesized parameter. (statistic - parameter)

Question 44

22 one-tailed tests

Answer 44

A alternative hypothesis where the researcher is interested in deviations in only one direction (“” is in Ha)

Question 45

22 two-tailed hypothesis

Answer 45

two sided alternative: An alternative hypothesis where the researcher is interested in deviations in both directions. (“≠” is in Ha.) Remember to always double the table probability when computing P-value for a two sided alternative.

Question 46

22 Practical Importance/significance

Answer 46

if a value has practical importance/significance the difference between the observed statistic and the claimed parameter value is large enough to be worth reporting.

To assess practical significance, look at the numerator of the test statistic and ask “Is the difference important?” If yes, then results are also of practical significance. (Note: Do not assess practical significance unless results are statistically significant.)