Question

In a sample of 7 cars each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results are obtained
0.18, 0.16, 0.08, 0.06,0.17,0.12,0.15 assuming that this sample is representative of the cars in use. cosntruct a 98% confidence interval estimate of the mean amount of nitrogen=oxide emissions for all cars. if the epa requires that nitrogen oxide emissions can be less than 0.165g.mi we can safely conclude that requirement is being met

A)what is the confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars
___g/mi 12 years ago

Answer 1

I have this same question! lol

Answer 2

The first step is to calculate the sample mean by adding the seven values and dividing by 7:
\[\bar{x}=\frac{0.18+0.16+0.08+0.06+0.17+0.12+0.15}{7}=\frac{0.92}{7}=0.13143\]

Answer 3

@kropot72, then how do you get the __g/mi <u< __g/mi ??

Answer 4

The next step is to calculate the sample standard deviation, s.

Answer 5

not sure how to do that..

Answer 6

You can use a calculator with statistical functions to calculate the sample standard deviation, s.

Answer 7

x= i got a totally different answer than you did

Answer 8

and the sd i think is 0.046

Answer 9

how did you get the sd @andijo76

Answer 10

@andijo76 what did you get for the sum of the seven data values?

Answer 11

i found a website back when i was doing pre algebra that helps me figuring out some calculations

Answer 12

the sum i got was 0.842/7=0.1203

Answer 13

does anyone know how to input this into the Ti84?

Answer 14

@andijo76 The correct sum of the seven data values is 0.92.

Answer 15

im trying to figure out how i got that lol

Answer 16

is the sd right tho

Answer 17

My calculator gives the value for the sample standard deviation of s = 0.4634

Answer 18

@kropot72 how did you input the sd in the calc?

Answer 19

My calculator is a Casio fx-82 AU PLUS. I just followed the instructions in the User's Guide.

Answer 20

im sorry you are correct i dont know what i did but i fixed it i think i rounded one decimal or something

Answer 21

there is a website that gives you sd i will paste what it said

Answer 22

Simplify the result.

σ=0.046344719225

The standard deviation should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

0.046

Answer 23

@andijo76 can you paste the link to the website?

Answer 24

www.mathway.com it costs 20 a month though i keep it for my kids it helps you figure out things step by step

Answer 25

The final calculation uses the following formula:
\[\bar{x}-2.576\frac{s}{\sqrt{n}}<\mu<\bar{x}+2.576\frac{s}{\sqrt{n}}\]
Substituting values gives the confidence interval for the population mean as follows:
\[0.13143-2.576\frac{0.046}{\sqrt{7}}<\mu<0.13143+2.576\frac{0.046}{\sqrt{7}}\]

Answer 26

where did you get the 2.576?

Answer 27

The value 2.576 is determined by an inverse normal technique. However it can be found in tables for use in calculating confidence intervals.

Answer 28

ok

Answer 29

i know i am going to sound stupid but how do i figure _g/mi<u<_g/mi was that the answer

Answer 30

When you have calculated the two values for the confidence interval, just put the lower value where the first underscore is and the higher value where the right hand underscore is.

Answer 31

i got for the first one -44.6558 so i am thinking it is i just have to put round and put it in 3 decimal places

Answer 32

so is this the answer then: .0866 g/mi< .1762 g/mi ?! @kropot72

Answer 33

Looks correct to me :)

Answer 34

yeah i forgot the point haha

Answer 35

it amazing how that works hey

Answer 36

It is a very powerful technique!

Answer 37

thank you so much for your help

Answer 38

You're welcome :)

Answer 39

lol great! thanks!!