Studied by 3 people

5.0(1)

Get a hint

Hint

1

sampling distribution of the sample mean

a probability distribution of all possible sample means of a given sample size from the same population

New cards

2

central limit theorem

As the size n of a simple random sample increases, the shape of the sampling distribution of x̄ tends toward being normally distributed

New cards

3

sampling distribution center

population parameter, equivalent to mu of population

New cards

4

sampling distribution spread

standard deviation decreases as sample size increases

New cards

5

natural variation

common/normal sources of chance variation that does not cause problems

New cards

6

unnatural variation

special causes or assignable sources of variation ex: bad batch of raw material, broken machine, poorly trained operator

New cards

7

statistical process control

a system in which management collects and analyzes information about the production process to pinpoint quality problems in the production system

New cards

8

x-bar control chart

statistical tool for monitoring a process that has variation, alerting us when a problem or unnatural variation has occurred (in which case process should be stopped and fixed)

New cards

9

in control process

process whose output exhibits only natural variation over time

New cards

10

out of control process

process exhibits unnatural variation

New cards

11

construction of x-bar control chart

draw horizontal centerline at μ

draw horizontal control limits at μ±3(σ/√3)

plot means from sample size n against time

New cards

12

out of control signals

point above/below control limits or nine consecutive points on the same side of the center line

New cards

13

inference

drawing conclusions about a population (parameter) based on data from a sample (statistic) with a measure of uncertainty

New cards

14

point estimation

data from the sample is used to estimate the population parameter; no measure of uncertainty; should only be used as step one in valid inference

New cards

15

interval estimation (confidence interval)

range of plausible values for population parameter; used for research questions asking for value

New cards

16

hypothesis testing (tests of significance)

states claim and checks whether sample data provides evidence for/against claim; used for research questions asking yes/no questions

New cards

17

accuracy of x-bar estimating μ

dependent on random sampling and distribution of x-bar (accuracy increases as sample size increases)

New cards

18

four steps for confidence intervals

state, plan, solve, conclude

New cards

19

confidence interval

estimate a parameter; value

New cards

20

test of significance

assess claim about a parameter; yes/no

New cards

21

conditions for inference

randomness, normal distribution, linear, no outliers, constant standard deviation

New cards

22

properties of t distributions

symmetric, bell shaped, mean=0, smaller degrees of freedom correlate to a larger spread, larger degrees of freedom correlates to be closer to the standard normal (z distribution)

New cards

23

format of t distribution table

degrees of freedom = n-1

use closest df without going over

t* values found in the body of table

New cards

24

outline for one-sample t confidence interval

state the problem

plan (procedure, confidence level, parameter of interest in context)

solve (collect/plot data, calculate x-bar and s, check randomness and normality/large population, calculate)

conclude (state confidence, parameter in context and calculated interval)

New cards

25

confident

percentage of confidence intervals produced by the procedure that actually contain μ; success rate of procedure

New cards

26

margin of error

likely maximum difference between the statistic and the parameter at the stated confidence level; accounts for uncertainty due to sampling variability only

New cards

27

properties of a confidence interval

margin of error (m) controls the width of the interval

as sample size increases, m and width decrease (more precise)

as sample size decreases, m and width increase (less precise)

New cards

28

when to use confidence intervals

randomness; normal population or large sample size

New cards

29

statistical inference

drawing conclusion about parameter using statistic with a measure of uncertainty

New cards

30

test of significance assumption

claim researchers think is not true; proof by contradiction

New cards

31

one sided test

a test with inequality in Ha

New cards

32

two sided test

a test with a not equal to in Ha

New cards

33

test statistic

a number that summarizes the data for a test of significance; compares estimate of parameter from sample data with parameter given in null hypothesis; measures how far sample data diverge from Ho; large values are not consistent with Ho and give evidence against; used to find probability of obtaining sample data if Ho were true

New cards

34

meaning of p-value

probability of getting a test statistic as extreme or more extreme than observed if Ho were true; measure of strength of agreement between observed test statistic and Ho (small = little agreement)

New cards

35

meaning of significance level (α)

pre-specified cutoff for p-value; boundary between rejection and non-rejection regions for p-value; if p-value is less than α, difference is statistically significant, reject Ho and conclude it's false

New cards

36

null hypothesis

always contains equality, claim we first assume is true and hope to disprove

New cards

37

alternative hypothesis

always contains inequality, claim we think is true and hope to prove by disproving Ho

New cards

38

p-value < α

statistically significant, reject Ho, sufficient evidence that Ha is true, difference between x-bar and claim is real

New cards

39

p-value > α

not statistically significant, fail to reject Ho, insufficient evidence that Ha is true, difference between x-bar and claim is due to chance

New cards

40

one-sample t-test for means

if SRS, unknown standard deviation, approximately normal population

then sampling distribution of equation has student's t-distribution with n-1 degrees of freedom

New cards

41

steps for one sample t-test

state problem (yes/no about quantitative)

plan (write Ho and Ha which both have mu, select α)

solve (compute test statistic and find p-value)

conclude (compare, fail/reject to fail, state sufficient/insufficient evidence in context)

New cards

42

standard error of x-bar

s/√n

New cards

43

margin of error for estimating mu

t*(s/√n)

New cards

44

p-value from t table

df determine correct row

follow columns on either side of test statistic and check for 1 or 2 sided test

p-value is given as a range of values

New cards

45

significance depends on

size of observed effect (numerator), how far sample mean deviates from hypothesized claimed mean, size of sample

New cards

46

large observed effect and large sample size effects

smaller p-value

New cards

47

sample size and significance

sample size may be too small to detect significance or sample size may be so large results are always significant

New cards

48

practical importance

determined by common sense, not the same as statistical significance and is checked after, especially important for large samples

New cards

49

statistical significance

p-value < α

New cards

50

practically important

observed effect (numerator of test statistic) matters in real life

New cards

51

p-value for a two sided test

equal to two times the p-value for a one-sided test; requires stronger evidence (smaller probability) than one-sided test

New cards

52

confidence interval approach to hypothesis testing

Ha is two sided; confidence level and significance level add to 100%

New cards

53

confidence interval does not contain claimed mean

reject Ho, test is statistically significant

New cards

54

confidence interval contains claimed mean

fail to reject Ho, test is not statistically significant

New cards

55

type I error

rejecting Ho when Ho is true; false positive; probability: α

New cards

56

type II error

fail to reject Ho when Ho is false; false negative; probability: β

New cards

57

power

reject Ho when it's false; probability = 1-β

New cards

58

safe

fail to reject Ho when it's true; probability = 1-α

New cards

59

relationship between α and power (fixed n)

decreasing α increases β and decreases power; increasing α decreases β and increases power

New cards

60

relationship between n and power (fixed α)

increasing n increases power and decreases β

New cards

61

relationship between effect size and power (fixed α)

larger effect size results in larger power

New cards

62

effect size

difference between actual μ and claimed μ

New cards

63

small level of significance (α)

requires larger sample

New cards

64

higher power

requires larger sample

New cards

65

detecting a small effect size

requires a larger sample

New cards

66

a two sided test requires

a larger sample than a one sided test

New cards

67

α

intentionally set low

New cards

68

β

want low; done by increasing α or n

New cards

69

1-β

want high; done by increasing α or n or having a small spread or large effect size

New cards