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Math 205: Elementary Statistics > Exam 2 > Flashcards

Exam 2 Flashcards

1
Q

process of drawing conclusions about the entire population based on information in a sample

A

statistical inference

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2
Q

a number that describes some aspect of a population

A

parameter

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3
Q

a number that is computed from the data in a sample

A

statistic

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4
Q

the sample statistic of the true value of the population parameter when we only have one sample and don’t know the value of the population parameter

A

best estimate

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5
Q

if μ = the mean commute time for workers in a particular city, what statistic would you use to estimate?

A

x-bar

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6
Q

if p = the size of dinner bills and size of tips at a restaurant, what statistic would you use to estimate?

A

r

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7
Q

distribution of sample statistics computed for different samples of the same size from the sample population

A

sampling distribution

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8
Q

if samples are randomly selected and sample size is large enough the distribution will be ______ and the centered at _____

A

symmetrical and bell-shaped
value of the population parameter

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9
Q

the standard deviation of the sample statistic

A

standard error

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10
Q

as sample size increases, variability of the sample statistic _____

A

decrease

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11
Q

how do you give a plausible range of values when you are given the margin of error and the sample statistic?

A

sample statistic +/- margin of error

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12
Q

what is the margin of error?

A

a number that reflects the precision of the sample statistic as an estimate for a parameter

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13
Q

an interval computed from sample data by a method that would capture the parameters for a specified proportion of all samples

A

confidence interval

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14
Q

success rate or the proportion of all samples whose intervals contain the parameter

A

confidence level

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15
Q

how do you determine the confidence interval from the standard error?

A

statistic +/- 2(SE)

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16
Q

difference between standard deviation and standard error?

A

standard deviation is of the individual sample
standard error would be if the mean of the sample units were computed over and over again

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17
Q

amount added and subtracted in a confidence interval

A

margin of error

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18
Q

standard deviation of the sample statistic if we could take many samples of the same size

A

standard error

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19
Q

how do you interpret the confidence interval?

A

we are sure that our interval contains the population parameter
“we are sure the parameter falls within these values”

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20
Q

sampling with replacement from the original sample using the same sample size

A

bootstrap sample

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21
Q

computing the statistic of interest for each of the bootstrap samples

A

bootstrap statistic

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22
Q

the statistic for many bootstrap samples

A

bootstrap distribution

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23
Q

how would you conduct a bootstrap sample from a jar of 100 nuts with 52 peanuts in it to find the proportion of peanuts in the jar?

A

shake the jar, pull a nut out, record if it is a peanut, put the nut back, and repeat 99 more times

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24
Q

if sample size is increased, precision of estimate is _____

A

increased

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25
Q

if sample size is increased, standard error _____

A

decreases

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26
Q

if sample size is increased, width of confidence interval _____

A

decreases

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27
Q

used to determine whether results from a sample are convincing enough to allow us to conclude something about the population

A

statistical tests

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28
Q

Ho - claim that there is no effect or no difference

A

null hypothesis

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29
Q

Ha - claim for which we seek significant evidence

A

alternative hypothesis

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30
Q

in a hypothesis test, we want to refute the _____ and support the _____

A

null hypothesis
alternative hypothesis

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31
Q

Ho and Ha describe the sample or population?

A

population

32
Q

what must always be present in a null hypothesis?

A

=

33
Q

for a hypothesis test, if there is one categorical variable, what is the parameter?

A

proportion
p

34
Q

for a hypothesis test, if there is one quantitative variable, what is the parameter?

A

mean
mu

35
Q

for a hypothesis test, if there is one categorical variable and one quantitative variable, what is the parameter?

A

difference in means
mu1-mu2

36
Q

for a hypothesis test, if there is two categorical variables, what is the parameter?

A

difference in proportions
p1-p2

37
Q

for a hypothesis test, if there is two quantitative variables, what is the parameter?

A

correlation
rho

38
Q

simulate many samples assuming the null hypothesis is true and collect the values of a sample statistic for each simulated sample

A

randomization distribution

39
Q

the randomization distribution will be centered at the ______

A

value indicated by the null hypothesis

40
Q

the farther out the observed sample statistic s in the tail of the randomization distribution, the ______ the evidence is against the null hypothesis

A

stronger

41
Q

proportion of samples when the null hypothesis is true that would give a statistic as extreme as or more than the observed statistic

A

p-value

42
Q

how do u find the p-value from the randomization distribution?

A

find the observed statistic in the randomization distribution

find the proportion of the simulated samples that have statistics as extreme as the statistic observed in the original sample
x-x

43
Q

sample statistics farther out in the tail give ____ p-values

A

smaller

44
Q

the smaller the p-value, the _____ the evidence is against the null hypothesis and in support of the alternative

A

greater

45
Q

how to write out the p-value explanation

A

there is a (p-value) change of a difference of proportion of (variable) of (null number) or more extreme if there was no difference in (variable testing)

46
Q

you generate a randomization distribution by _______

A

assuming the null is true
(putting null in the center)

47
Q

shows how extreme the difference in statistics is

A

p-value

48
Q

if the p-value is small enough, then results as extreme as the observed statistic are ____ to occur by random chance alone and we say that the sample _____ statistically significant

A

unlikely
is

49
Q

if our sample if statistically significant, we have convincing evidence that _________

A

against Ho and in favor of Ha

50
Q

the significance level a for a test of hypotheses is a boundary below which we conclude that a p-value shows ______

A

statistically significant evidence against the null

51
Q

if significance level is not specified, we use a=

A

0.05

52
Q

if p<a,

A

reject Ho
results are significantly significant and we have convincing evidence that Ha is true

53
Q

is p> or equal to a,

A

do not reject Ho
results are not significantly significant and we do not have convincing evidence Ha is true

54
Q

note: if p value is small enough then it is not likely to happen by random chance if the null is true

A
55
Q

smaller p value is better/worse?

A

better!

56
Q

what is a type 1 error?

A

rejecting a true Ho

57
Q

what is a type II error?

A

accepting a false Ho

58
Q

if you reject a true Ho, what kind of error is that?

A

type I

59
Q

if you accept a false Ho, what kind of error is that?

A

type II

60
Q

represents a tolerable probability of making a type I error

A

significance level

61
Q

with a larger sample size, it is _____ to find a significant result

A

easier

62
Q

what is 1-β

A

power
chance/probability of not making a type II error

63
Q

how can you reduce the probability of a type I error?

A

decreasing the significance level

64
Q

how can you reduce the probability of a type II error?

A

increase the significance level or sample size

65
Q

when you test the same data a lot, the chance of type I error _____ overall

A

increases

66
Q

shows the distribution of sampling statistics from a population, and is generally centered at the true value of the population parameter

A

sampling distribution

67
Q

simulates a distribution of sample statistics for the population, but is generally centered at the value of the original sample statistic

A

bootstrap distribution

68
Q

simulates a distribution of sample statistics for a population in which the null hypothesis is true, and is generally centered at the value of the null parameter

A

randomization distribution

69
Q

the formal decision for a two-tailed hypothesis is related to

A

whether the null parameter falls within a confidence interval

70
Q

when the parameter value given in Ho falls _____ of a 95% confidence interval, then it is not a plausible value for the parameter and we should reject Ho at a 5% level in a two-tailed test

A

outside

71
Q

when the parameter value given in Ho falls _____ of the 95% confidence interval, then it is a plausible value for the parameter and we should not reject Ho at a 5% level in a two-tailed test

A

inside

72
Q

bootstrap simulates population centered at sample stat - bell shaped

A

confidence interval

73
Q

simulate null hypothesis and centered at null - bell shaped

A

hypothesis test

74
Q

if null is not in the confidence interval, then we

A

reject Ho

75
Q

a probability needs to be between

A

0 and 1

Math 205: Elementary Statistics (3 decks)

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