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Type 1 errors | Inferential statistics | Probability and Statistics | Khan Academy

Video vocabulary

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

type

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US / taɪp /

UK / taɪp /

A1
  • noun
  • Printed letters or blocks used for printing them
  • Group of things or people sharing common features
  • verb
  • To identify something belonging to a group
  • To write by touching keys on a keyboard

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

case

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US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

great

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US / ɡreɪt /

UK / ɡret /

A1
  • adjecitve
  • Very large in size
  • Very important
  • Very good; fantastic; wonderful
  • adverb
  • Very good; better than before
  • noun
  • Successful and well-admired person

happen

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US / 'hæpən /

UK / ˈhæpən /

A1
  • verb
  • To take place or occur

even

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US / 'i:vn /

UK / ˈivən /

A1
  • adjecitve
  • Being equal in influence, power, possibility etc.
  • Being divided equally or fairly
  • (Of teams/contest) with similar chances of success
  • Smooth, level, or regular
  • Can be divided by 2; ending in 2, 4, 6, 8, or 0
  • At a regular, equally steady manner
  • Remaining steady and unchanging
  • adverb
  • (When this is surprising) as well; too
  • (Used to compare two things/stress the difference)
  • verb
  • To make something level; to flatten
  • To make something equal

value

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US / 'vælju: /

UK / ˈvælju /

A1
  • noun
  • Importance you attach to something
  • Some information expressed as a number
  • Stated price of something; worth
  • verb
  • To place a high importance on something
  • To say how much money something is worth

example

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US / ɪgˈzɑ:mpl /

UK / ɪɡˈzæmpəl /

A1
  • noun
  • Thing, person which represents a category

enough

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US / ɪˈnʌf /

UK / ɪˈnʌf /

A1
  • adjecitve
  • Sufficient to answer the need
  • adverb
  • To a satisfactory degree
  • pronoun
  • Equal to what is needed; as much as required
  • Adequate number or amount

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

notion

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US / ˈnəuʃən /

UK / ˈnoʃən /

B1
  • noun
  • Sudden idea or desire to do something

quick

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US / kwɪk /

UK / kwɪk /

A1
  • adjecitve
  • Using very little time; moving far in little time
  • Learning and understanding rapidly and easily

true

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US / tru: /

UK / tru: /

A1
  • adjecitve
  • Agreeing with the facts; not false; real or actual

always

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US / 'ɔ:lweɪz /

UK / ˈɔlwez,-wɪz,-wiz /

A1
  • adverb
  • For a very long time
  • At all times; in every situation
  • For ever

previous

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US / ˈpri:viəs /

UK / ˈpriviəs /

A2
  • adjecitve
  • Existing or happening before the present time

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

extreme

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US / ɪk'stri:m /

UK / ɪkˈstrim /

B1
  • adjecitve
  • Very great in degree
  • Farthest from a center
  • Very severe; very strong
  • noun
  • Effort that is thought more than is necessary

area

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US / 'eərɪə /

UK / ˈɛriə /

A1
  • noun
  • Amount of measured space
  • A specific section or space; part of a region
  • A subject or field of study

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

threshold

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US / 'θreʃhəʊld /

UK / ˈθrɛʃˌold, -ˌhold /

B2
  • noun
  • Degree or level at which something begins

start

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US / stɑ:t /

UK / stɑrt /

A1
  • noun
  • First time or place that a thing exists; beginning
  • First opportunity to achieve something, e.g. a job
  • Sudden action or movement because you are scared
  • other
  • Beginning of something in place or time
  • verb
  • To do, be or happen for the first time; begin
  • To turn something on

much

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US / mʌtʃ /

UK / mʌtʃ /

A1
  • adjecitve
  • Very; to a high level or degree
  • adverb
  • A lot; large amount; a high degree of
  • Nearly; basically
  • On many occasions; often
  • noun
  • A large amount; a great quantity

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

clarify

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US / 'klærəfaɪ /

UK / ˈklærəˌfaɪ /

B1
  • verb
  • To make a liquid become clear or pure
  • To state again so that a point is clearer

though

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US / ðəu /

UK / ðo /

A1
  • adverb
  • Although, despite the fact that

probability

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US / ˌprɒbəˈbɪləti /

UK / ˌprɑ:bəˈbɪləti /

A2
  • noun
  • What the chances are that something will happen

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

reject

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US / rɪˈdʒekt /

UK / rɪˈdʒɛkt /

A2
  • noun
  • Goods that are not suitable for sale at full price
  • Person others do not like, or refuse to accept
  • verb
  • To decide that something is not good enough
  • To refuse, deny to believe, accept, or consider

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

maybe

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US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

video

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US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

testing

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US / ˈtestɪŋ /

UK / ˈtestɪŋ /

A1
  • verb
  • To be given a medical examination
  • To try to establish the truth or nature of
  • To ask a series of questions to measure knowledge

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

usually

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US / ˈju:ʒuəli /

UK / ˈjuːʒuəli /

A1
  • adverb
  • Normally; regularly

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

gee

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US / dʒi: /

UK / dʒi /

C2
  • exclamation
  • Give a command to a horse to turn to right
  • Used to express concern or surprise

tackle

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US / 'tækl /

UK / ˈtækəl /

B1
  • noun
  • Equipment used in fishing
  • Arrangement of ropes and wheels used for lifting
  • Attempt to force a person to the ground
  • verb
  • To start working on a difficult problem
  • To grab and throw a person to the ground

result

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US / rɪ'zʌlt /

UK / rɪˈzʌlt /

A2
  • noun
  • Something produced through tests or experiments
  • Final score of a competition, election or game
  • verb
  • To be the outcome of other causes and effects

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

error

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US / ˈerə(r) /

UK / ˈɛrɚ /

A2
  • noun
  • Something that is not correct; a mistake

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

chance

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US / tʃɑ:ns /

UK / tʃæns /

A1
  • adjecitve
  • Happening by luck; not planned
  • Taking a risk to try something
  • noun
  • The way something happens without planning
  • An opportunity; favorable circumstances, situation
  • The possibility that something will happen
  • verb
  • To occur just through luck; happen
  • To take a risk to try something

look

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US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

confusing

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US / kənˈfju:zɪŋ /

UK / kənˈfjuzɪŋ /

A2
  • adjecitve
  • Being hard to understand
  • verb
  • To make something unclear or hard to understand

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

low

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US / ləʊ /

UK / lo /

A1
  • adjecitve
  • Having a small quantity, supply, or amount
  • Being unhappy or unpleasant in attitude
  • Not high; being near the ground, or bottom
  • (Of a voice, sound) being soft; quiet
  • noun
  • Situation of not having a lot of something

sample

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US / ˈsɑ:mpl /

UK / ˈsæmpl /

A2
  • noun
  • A small quantity of something used as a taster
  • verb
  • To try (e.g. food, drink), to see if you like it

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

clear

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US / klɪə(r) /

UK / klɪr /

A1
  • adjecitve
  • Empty; without anything in it or on it
  • Being certain and without doubt
  • Being without any streaks, spots, or cracks
  • Easy to understand; well-explained; obvious
  • adverb
  • Completely; entirely; through the whole of
  • Away from; free from
  • verb
  • To recover from or remove a problem
  • To get rid of the entire contents of
  • To give permission for something to happen
  • To make a place or surface empty by removing
  • To prove that someone is not guilty or to blame

unlikely

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US / ʌnˈlaɪkli /

UK / ʌnˈlaɪkli /

A2
  • adjecitve
  • Not seeming suitable for a particular purpose
  • adverb
  • Not likely to happen; not likely to be the truth

know

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US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

less

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US / les /

UK / lɛs /

A1
  • adjecitve
  • Smaller in amount or degree
  • adverb
  • To a smaller degree
  • noun
  • A smaller amount
  • preposition
  • With the subtraction of

statistic

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US / stəˈtɪstɪk /

UK / stəˈtɪstɪk /

B1
  • noun
  • Number that represents a piece of information

null

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US / nʌl /

UK / nʌl /

B2
  • adjecitve
  • Having no impact; ineffective; cancelled out

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

might

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US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

only

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US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

normally

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US / ˈnɔ:məli /

UK / ˈnɔːrməli /

B1
  • adverb
  • In the manner that is usual or ordinary

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

another

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US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

decide

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US / dɪ'saɪd /

UK / dɪˈsaɪd /

A2
  • verb
  • To make a choice or choose after thinking about it
  • To make a legal judgment in court
  • to affect the result of something

hopefully

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US / ˈhəʊpfəli /

UK / ˈhopfəli /

A2
  • adverb
  • In a manner wishing something to happen

sometimes

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US / ˈsʌmtaɪmz /

UK / ˈsʌmˌtaɪmz /

A1
  • adverb
  • Only at certain times; occasionally

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something
  • Subtitles section
  • I want to do a quick video on something that you're likely to see in a statistics class, and that's the notion of a Type 1 Error.
  • And all this error means is that you've rejected-- this is the error of rejecting-- let me do this in a different color-- rejecting the null hypothesis even though it is true.
  • So for example, in actually all of the hypothesis testing examples we've seen, we start assuming that the null hypothesis is true.
  • We always assume that the null hypothesis is true.
  • And given that the null hypothesis is true, we say OK, if the null hypothesis is true then the mean is usually going to be equal to some value.
  • So we create some distribution.
  • Assuming that the null hypothesis is true, it normally has some mean value right over there.
  • Then we have some statistic and we're seeing if the null hypothesis is true, what is the probability of getting that statistic, or getting a result that extreme or more extreme then that statistic.
  • So let's say that the statistic gives us some value over here, and we say gee, you know what, there's only, I don't know, there might be a 1% chance, there's only a 1% probability of getting a result that extreme or greater.
  • And then if that's low enough of a threshold for us, we will reject the null hypothesis.
  • So in this case we will-- so actually let's think of it this way.
  • Let's say that 1% is our threshold.
  • We say look, we're going to assume that the null hypothesis is true.
  • There's some threshold that if we get a value any more extreme than that value, there's less than a 1% chance of that happening.
  • So let's say we're looking at sample means.
  • We get a sample mean that is way out here.
  • We say, well, there's less than a 1% chance of that happening given that the null hypothesis is true.
  • So we are going to reject the null hypothesis.
  • So we will reject the null hypothesis.
  • Now what does that mean though?
  • Let's say that this area, the probability of getting a result like that or that much more extreme is just this area right here.
  • So let's say that's 0.5%, or maybe I can write it this way.
  • Let's say it's 0.5%.
  • And because it's so unlikely to get a statistic like that assuming that the null hypothesis is true, we decide to reject the null hypothesis.
  • Or another way to view it is there's a 0.5% chance that we have made a Type 1 Error in rejecting the null hypothesis.
  • Because if the null hypothesis is true there's a 0.5% chance that this could still happen.
  • So in rejecting it we would make a mistake.
  • There's a 0.5% chance we've made a Type 1 Error.
  • I just want to clear that up.
  • Hopefully that clarified it for you.
  • It's sometimes a little bit confusing.
  • But we're going to use what we learned in this video and the previous video to now tackle an actual example.