Ch 9/Ch 11: Testing Claims about Proportions/Means

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significance test

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43 Terms

1

significance test

 a formal procedure for using observed data to decide between two competing claims (called hypotheses) about given parameters

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2

null hypothesis (Ho)

the claim that we weigh evidence against in a significance test

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3

alternative hypothesis (Ha)

the claim that we are trying to find evidence for

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4

one-sided alternative hypothesis

states that a parameter is greater than the null value or if it states that the parameter is less than the null value

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5

two-sided alternative hypothesis

 states that the parameter is different from the null value (it could be either greater than or less than)

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6

always state null and alternative hypotheses in terms of ______________

population parameters (NOT sample statistics)

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7

if the p-value is less than or equal to the significance level (alpha)

reject Hand conclude there is convincing evidence for Ha (in context)

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8

if the p-value is greater than the significance level (alpha)

fail to reject Hand conclude there is not convincing evidence for Ha (in context)

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9

significance level α

 the value that we use as a boundary for deciding whether an observed result is unlikely to happen by chance alone when the null hypothesis is true

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10

Type I error

 if we reject Ho  when His true —> the data give convincing evidence that Ha is true when it really isn’t

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11

Type II error

occurs if we fail to reject Ho when Ha is true —> the data do not give us convincing evidence that Ha is true when it really is

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12

probability of a type __ error is equal to the significance level

I

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13

Ho true, reject Ho = _____ error

type I

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14

Ha true, fail to reject Ho = _____ error

type II

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15

Ho true/fail to reject Ho OR Ha true/reject Ho

correct conclusion

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16

relationship between type I and type II errors

s the probability of a Type I error increases, the probability of a Type II error decreases

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17

type I error is also known as a false ______

positive

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18

type II error is also known as a false ______

negative

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19

condition for significance test about a proportion - RANDOM

 the data come from a random sample from the population of interest

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20

condition for significance test about a proportion - INDEPENDENT

10% condition: n < 0.10N

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21

condition for significance test about a proportion - NORMAL

large counts condition → both np0 and n(1-p0) are at least 10.

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22

p0

 our hypothesized population proportion (aka the proportion we are assuming is true in our null hypothesis)

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23

standardized test statistic

measures how far a sample statistic is from what we would expect if the null hypothesis were true, in standard deviation units

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24

equation for standardized test statistic

(statistic-parameter)/standard deviation (error) of statistic

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25

standardized test statistic if we KNOW the population standard deviation is ___

z

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26

standardized test statistic if we DO NOT KNOW the population standard deviation is _____

t

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27

power

the probability that the test will find convincing evidence for Ha when a specific alternative value of the parameter is true OR probability that we find convincing evidence that the alternative hypothesis is true, given that the alternative hypothesis really is true

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28

equation for power

Power = 1 - P(Type II Error)

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29

equation for probability of type II error

P(Type II Error) = 1 - Power

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30

to increase power:
______ sample size (n)
______ significance level (α)

_______ distance between null and alternative parameter values

INCREASE

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31

condition for performing a significance test about a difference between two proportions (RANDOM)

the data come from two independent random samples or from two groups in a randomized experiment

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32

condition for performing a significance test about a difference between two proportions (INDEPENDENT)

10% condition: n1 < 0.10N AND n2 < 0.10N

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33

condition for performing a significance test about a difference between two proportions (NORMAL)

 Large Counts Condition: expected numbers of successes and failures in each sample or group are all at least 10 (use p-hat cbmbined)

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34

equation for p-hat combined

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" data-is-equatio="1" data-latex="\hat{p}_c=\ \frac{X_1+X_2}{n_1+n_2}"><msub><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo stretchy="false">^</mo></mover></mrow><mi>c</mi></msub><mo>=</mo><mtext></mtext><mfrac><mrow><msub><mi>X</mi><mn>1</mn></msub><mo>+</mo><msub><mi>X</mi><mn>2</mn></msub></mrow><mrow><msub><mi>n</mi><mn>1</mn></msub><mo>+</mo><msub><mi>n</mi><mn>2</mn></msub></mrow></mfrac></math>

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35

the Normal condition for a significance test about a mean can be satisfied in these 3 ways:

 1) told the population is Normal

2) n is large (greater than 30, per the CLT)

3) graph and sketch a dotplot/histogram and assess shape (look for massive skew or outliers)

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36

formula for one-sample t-test for means

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" data-is-equatio="1" data-latex="t=\frac{\overline{x}-\mu_0}{\frac{s_x}{\sqrt{n}}}"><mi>t</mi><mo>=</mo><mfrac><mrow><mover><mi>x</mi><mo accent="true">―</mo></mover><mo>−</mo><msub><mi>μ</mi><mn>0</mn></msub></mrow><mfrac><msub><mi>s</mi><mi>x</mi></msub><msqrt><mi>n</mi></msqrt></mfrac></mfrac></math>

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37

in what situation should you select “pooled” on your calculator?

NEVER

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38

equation for degrees of freedom

df = n-1

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39

inference procedure for paired data

one-sample t procedures for mean difference

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40

inference procedure for quantitative data from independent random samples of two populations of interest/groups in a randomized experiment

twp-sample t-tet for mu1-mu2

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41

if a condition is NOT met…

"although this condition has not been satisfied,

we will assume that it has been, and proceed

with caution."

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42

characteristics of a paired t test

-one sample (data are paired)

-mean of differencces

-subtract, then average

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43

characteristics of a two-sample t test

-two independent samples/groups

-difference of means mu1-mu2

-average, then subtract

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