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MA223—Elementary Probability & Statistics > Exam 3 > Flashcards

Exam 3 Flashcards

1
Q

point estimate

A

single number that is our “best guess” for a parameter

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2
Q

properties of good estimators (3)

A
  1. sampling distribution centered at parameter (unbiased)
  2. small standard deviation
  3. relatively efficient (small variance)
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3
Q

interval estimate

A

interval within which the parameter is believed to fall

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4
Q

2 properties that define interval estimate

A

margin of error
confidence level

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5
Q

margin of error

A

measures how accurate the point estimate is likely to be

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6
Q

confidence level

A

probability of interval containing the parameter

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7
Q

formula for interval for μ, assuming that σ is known

A
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8
Q

3 common confidence levels with z(𝛼/2)

A
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9
Q

correct way to describe conclusion with a confidence interval

A

with –% confidence, we can say that the interval contains the parameter

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10
Q

formula for minimum sample size needed for an interval estimate of μ

A

E = margin of error

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11
Q

way to get crude σ if not given

A

σ ≈ range/6

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12
Q

formula for interval for μ, assuming σ is not known

A
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13
Q

as n ↑, t ….

A

approaches z (standard normal distr)

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14
Q

point estimate for pop proportion

A

p hat

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15
Q

formula for p hat, q hat

A
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16
Q

formula for interval for p

A
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17
Q

formula for minimum sample size needed for proportion

A
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18
Q

if p hat is not given on sample size problem…

A

use p hat = 0.5

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19
Q

chi square characteristics

A

right skewed
area = 1.00
no negatives

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20
Q

“left” chi value

A

x^2 (1-𝛼/2)

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21
Q

“right” chi value

A

x^2 (𝛼/2)

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22
Q

formula for σ interval

A
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23
Q

for what CI is chi square used?

A

variance/std dev

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24
Q

chi value 𝛼 gives area to the….

A

right of the critical value

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25
Q

3 methods of HT

A

traditional method
p-value method
confidence interval method

26
Q

hypothesis

A

statement about a population, usually of the form that a certain parameter takes a particular numerical value or falls in a certain range

27
Q

null hypothesis states…

A

that there is no difference between parameter and value

28
Q

alternative hypothesis states…

A

that there is a difference between parameter and value

29
Q

conclusion language if claim is H0

A

“enough/not enough evidence to reject”

30
Q

conclusion language if claim is H1

A

“enough/not enough evidence to support”

31
Q

type II error
symbol

A

H0 is not true, but you fail to reject H0
β

32
Q

type I error
symbol

A

H0 is true, but you reject it
𝛼

33
Q

default 𝛼 for HT

A

0.05

34
Q

when to use right tail test

A

H1: parameter > #

35
Q

when to use left tail test

A

H1: parameter < #

36
Q

when to use two tail test

A

H1: parameter ≠ #

37
Q

traditional HT method steps

A

1) hypotheses & claim
2) critical values
3) test statistic
4) decision
5) conclusion

38
Q

formula to generate z test stat for HT

A
39
Q

p-value

A

area of rejection region(s)
probability of getting an extreme sample statistic in the direction of H1

40
Q

in the p-value method you presume…

A

H0 is true

41
Q

how to find p-value

A

z table or normalcdf

42
Q

p-value decision rule

A

reject H0 if p-val < 𝛼

43
Q

low p-value increases probability of…

A

H1 being true

44
Q

T-test method of HT used when…

A

σ is unknown

45
Q

formula to generate t test stat for HT

A
46
Q

use for proportion HTs

A

z-test

47
Q

formula to generate z test stat for proportion HT

A
48
Q

chi-square is used for HT for which parameter?

A

σ or σ^2

49
Q

formula to generate chi test stat for variance HT

A
50
Q

2 tests used on qualitative variables

A

goodness of fit
test for independence

51
Q

GOF used when…

A

there is one variable

52
Q

what question does GOF answer?

A

how well does observed data fit what is expected?

53
Q

formula to generate chi test stat for GOF and TFI

A
54
Q

GOF and TFI use ——- distribution

A

chi square

55
Q

DF for GOF

A
56
Q

H0 and H1 for GOF

A

H0: p1 = #, p2 = #, etc
H1: at least one proportion is different

57
Q

TFI used when…

A

there are more than one variable in a contingency table

58
Q

what question does TFI answer?

A

is there a relationship between the variables?

59
Q

DF for TFI

A
60
Q

H0 and H1 for TFI

A

H0: no relationship/independent
H1: there is a relationship/dependent

61
Q

how to find expected values in each cell for TFI

A
62
Q

cell notation

A

MA223—Elementary Probability & Statistics (3 decks)

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