## andijo76 one year ago 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<u<___g/mi

1. StClowers

I have this same question! lol

2. kropot72

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

3. StClowers

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

4. kropot72

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

5. StClowers

not sure how to do that..

6. kropot72

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

7. andijo76

x= i got a totally different answer than you did

8. andijo76

and the sd i think is 0.046

9. StClowers

how did you get the sd @andijo76

10. kropot72

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

11. andijo76

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

12. andijo76

the sum i got was 0.842/7=0.1203

13. StClowers

does anyone know how to input this into the Ti84?

14. kropot72

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

15. andijo76

im trying to figure out how i got that lol

16. andijo76

is the sd right tho

17. kropot72

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

18. StClowers

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

19. kropot72

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

20. andijo76

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

21. andijo76

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

22. andijo76

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

23. StClowers

@andijo76 can you paste the link to the website?

24. andijo76

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

25. kropot72

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: $0.13143-2.576\frac{0.046}{\sqrt{7}}<\mu<0.13143+2.576\frac{0.046}{\sqrt{7}}$

26. StClowers

where did you get the 2.576?

27. kropot72

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

28. StClowers

ok

29. andijo76

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

30. kropot72

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.

31. andijo76

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

32. StClowers

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

33. kropot72

Looks correct to me :)

34. andijo76

yeah i forgot the point haha

35. andijo76

it amazing how that works hey

36. kropot72

It is a very powerful technique!

37. andijo76

thank you so much for your help

38. kropot72

You're welcome :)

39. StClowers

lol great! thanks!!