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95% Confidence Interval



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hey guys mr. Barnes here and I promised

you I'd take you through a confidence

interval equation so I'm going to do

just that so we got a question here from

an old common 2010 and it says Wilson's

Electronics claims that their new line

of plasma televisions will last for

6,000 60,000 hours a consumer research

group besides a claim test that claim

and they randomly select 50 televisions

to test and the data from the sample

shows that the mean life of television

is 57,000 hours with a standard

deviation of 1200 hours and yet 50 TVs

so this is determining 95 percent

conference in all four to mean life tell

me alrighty so we got a few numbers here

so what we have is my 50 televisions

that's my sample size so we call the

sample size in okay so we have n is

equal to 50 and then we have my mean or

my mu okay that is equal to 57,000

actually that should be X bar because mu

is for a population we're just going to

use X bar X bar that's for a sample and

then my standard deviation s X is equal

to 1200 hours okay so what we are going

to do is we're going to calculate the

conference in a 95% confidence interval

so I get 95% see I recognize that this

95% that I write here CI is not a number

it's not something that we need to you

you know change around and multiply

something no that's just 95 percent

conference know what we get to the right

hand side is what we need okay so we

have a 95% confidence interval and

that's going to be equal to my x-bar

plus or minus

1.96 all over s of X divided by or sorry

times at this X all over square root of

n okay so this is my 95 percent

conference interval and what this plus

or minus means basically we do with the

- we do with the plus so what we end up

having to do is we go X - I put the sort

of put this in brackets X minus 1.96

times standard deviation all over the

square root of n comma X bar plus 1.96 s

of x over square root of n so again this

is just the formula something that you

need to know and recognize that the

confidence interval is a range of

numbers it gives us we're not sure where

that mean is - but we know it's between

these two numbers somewhere in between

so we're confident that it's in between

these or 95% confident actually that

it's in between these two numbers so

what we need to do is we need to pick

this stuff every question and we need to

fill it in

okay so we have 57,000 is my X bar minus

1.96 times 1200 divided by the square

root of 50 now recognize for confidence

interval you need to have a sample size

greater than 30 if you don't you cannot

do it okay and the larger your sample

size the more accurate you know your

confidence interval or the less margin

of error as they say okay the mo as we

call it in class right

okay so this is my conference table now

I need to calculate that so I'm not a

not about to risk my mental math here

today so I'm going to I'm going to

calculate this so important recognize I

do what's left or sorry what's right of

this subtraction sign first

good old bad mess

okay so my this hair part as we called

it before if you remember this part

right here this is our mole our margin

of error okay so we calculate the margin

of error which we just do anyway when

we're doing conferencing okay there's

nothing more complicated than that we do

it anyway so let's we call 333 I'm going

to round there okay so I have 5 7

subtract 3 3 3 comma 5 seven zero zero

so 57,000 and recognize that this here

is the same as this number so I just

basically add on the MOE again so

recognize that the confidence interval

is just the mean plus or minus the

moment and the mole comes from this so

so I'm going to ask you what's the

margin of error of this conference

interval you calculate this part okay so

if someone asks this question what is

the mean of this particular situation or

sorry what is the mole of this

particular situation it's 333 that's the

margin of error

okay our mean varies by that much okay

that's our range so we do this again so

we're going to have five um six six six

the way

okay I got something missed up here I

got to fix this so that's a three three

like that so that should be a comma okay

kind of messy here gonna slow down a bit

and comma five seven three three three

so that's my confidence interval so

that's my conference interval and I just

noticed a mistake as per usual okay you

got your seven there I mental math Lou

laughs today I'm kind of tired so that's

my confidence interval okay

it goes from fifty six thousand six

hundred and seventy sixty seven and

fifty six thousand three hundred thirty

three so that is where I'm confident

where my mean number of hours lies

between okay so I just calculated

confidence interval now there's a B part

to this question and I want you to

recognize first of all what this is the

company says that their their line of

products will last for six hundred sixty

thousand hours so that's important the

company says it will ask for six

thousand dollars they did a test and set

the Amin was fifty seven so the second

part of the question asked me it says

will does the confidence interval

support the claim of Wilson's

Electronics let me just copy over oops

let me just copy over oh my god let me

just copy over my conference interval

there so this thing right here let me

copy that over so I'm going to copy

bring it over

paste it down so that's my confidence

interval there and remember the claim

was sixty thousand hours now sixty

thousand does not lie in this range okay

so the confidence interval does not

support okay

does not support and the reason being

is because 260 thousand nine this range

okay if they said that they thought it

lasts 57,000 then we'd be in business

this would be yes it does support but

that what their claim they're making is

not supported by the data found by this

company that did the research okay so

keep that in mind that there are some

conclusions we can draw from this

confidence interval all right guys I

hope I clear that up make sure you know

that formula it's important I guarantee

there's going to be a question on there

happens every year so make sure that you

know how to do this stuff okay easy

marks right there buddy all right thank

you very much bye-bye