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90% Confidence Interval



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hey guys mr. B here bring you another

math videos spice up your academic lives

this one is on the ninety percent

confidence interval and I've done two

actually on the 95 percent confidence

interval and I thought I'd throw this

one out there because a couple people

have commented that's what they they

were looking for and they didn't

couldn't find anything on YouTube or

anything suitable so I thought I'd do

one so if you want to look at the 95

percent counterfeit confidence interval

you can and then come back to this one

they're really much the same to

calculate but again a conference

interval is you know it's a range of

numbers and you know when we do an

experiment or you know we're collecting

data we want to have we're not going to

be able to do a survey of the whole

entire population whether trees people

whatever we're looking at so we want to

have with a certain we don't have a man

of certainty where a sample mean lies so

confidence circle gives us that it's a

range of numbers what where we think the

actual population mean will lie so we'll

know the sample mean we want to know is

the population mean what's our

confidence level of the population mean

being in this range of numbers so for a

normally distributed set of data what we

hope happens is that ninety percent of

the values are within one point six four

five you can ignore this part one point

six four five standard deviations of the

mean

okay which is approximately two that's

why I had there and I had that there for

95% confidence interval anyway 1.645 is

the number that we should be looking for

so within one point six four five

standard deviations and mean that's

where our population our population

parameter population mean should lie so

we can use this formula to calculate the

90% in confidence interval so 90 percent

confidence interval is equal to this the

sample mean I use the symbol x-bar

depends on my prof. users you can use

whatever you use plus or minus one point

six four five so that's our Z value

textbook that I refer to calls it times

the standard deviation of the sample

divided by the square root of the sample

size n so that's standard deviation

square root of sample size population or

sorry sample mean so we can use this

formula to do pretty much any question

as long as we have those three things

now I'm not going to go into how we

calculate standard deviation I'm just

gonna have a question it's already given

that that's out there on youtube if you

want to go ahead and search it maybe

I'll make a video on it later on so

before we do an example here's a

question on our Soria a question I get

very often is how to calculate the

margin of error so the margin of error

all it is is and I call it mo and our

honor of the mo from The Simpsons

it's basically 1.645 it's basically this

guy right here right 1.645 times a

standard deviation divided by the square

root of n so I mean it's a really simple

calculation all you need to get the

margin of error is the standard

deviation of the sample size and the

sample square root of the sample size

that's it so it's just whatever you add

on him here and we're gonna calculate

that when we do our examples all right

so let's do this example

so says Alex collects a random sample

size of 72 and finds that the sample

mean is 300 232 and the sample standard

deviations 18 calculate or determine the

90% confidence interval and explain what

the interval this interval represents

apparently I can't read today all right

so let's do it so our formula 90% C I is

equal to X bar plus or minus 1.645

divided by sample standard deviation of

samples sample and then square root of

the sample size so I end up with the

sample mean here is 300 232 232 plus or

minus one point

6 4 5 and then sample size is 72 so

divided by square root of 72 and then

sample standard deviation is 18 so I'll

break out my calculator ease 18 divided

by the square root of 72 times 1.645 so

I get to 32 plus or minus 3.4 I go for 9

all right so right here this number

right here that's my margin of error moe

and when we're calculating the of course

the conference in any conference

interval you need to do the plus in the

minus so it gives us a range number so

sometimes you might want to listen like

that so we're gonna have the minus 1

over here the smaller number and the

bigger number so 2 32 2 32 minus 3 point

4 9 and that's going to give us two

hundred and twenty eight point five one

and then two 32 plus three point four

nine and that gives us two thirty five

point four nine I'm just gonna double

check that number for one second there I

don't want to give you guys some bad

information not we're good that's good

all right so there it is so that's our

90% confidence in a soup

it says explain what the interval means

it means that we're 90 percent confident

that our population mean is between two

hundred twenty-eight point five one and

two hundred and thirty five point four

nine so that's it right so a 90%

confidence interval

it's gonna be smaller than a non e than

a 95% confidence interval because we're

less confident because the the range is

not as big we're less confident that the

population mean is gonna be in there so

keep that in mind alright so here's a I

guess a more tangible example someone's

doing a pH experiment on an altar doing

water samples from 5060 different rain

in one province were analyzed for

acidity pH the pH readings had a mean of

6.1 so there's money so that's the

sample mean and a standard deviation 0.4

determine and that's my sample size 60

determine the 90% confidence interval

for the mean and explain what this

interval represents so a very similar

question to the last one so what I have

is 90% see I is with x-bar plus or minus

1.645

standard deviation of the sample square

root of the sample size

let's fill her in so I got 6.1 plus or

minus one point six four five standard

deviation is 0.4 and then square root of

sample size 60 so then let's just do the

math on that so let's find the margin of

error first 1.645 times 0.4 divided by

square root of the sample size so very

small margin of error six point one

because you know we're dealing with

smaller numbers here zero decimal zero

eight five sort that all right so then

this is the margin of error here zero

point zero point zero eight five so

let's subtract it and then add it six

point one subtract zero decimal zero

eight five six point I guess I should

have known that off the top of my head

yes sir and then let's do the same thing

six point one plus zero decimal zero

eight five when I'm making videos I do

not like to make mistakes so I sort of

rely on my calculator a little bit too

much when I'm in class I feel I make

tons of mistakes doing the mental math

so don't worry about it alright so there

it is

that's you know a little mass a little

math I should say math free this morning

hopefully guys this makes sense to you

you say these aren't overly complex

examples you're probably gonna run in

the harder ones but this gives you the

gist and some basic information on how

to use the

so I hope this helps you you got

questions feel free to fire away I'll

see you guys in class

and hopefully you subscribe I'll talk