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andijo76

  • 10 months 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

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  1. StClowers
    • 10 months ago
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    I have this same question! lol

  2. kropot72
    • 10 months ago
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    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
    • 10 months ago
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    @kropot72, then how do you get the __g/mi <u< __g/mi ??

  4. kropot72
    • 10 months ago
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    The next step is to calculate the sample standard deviation, s.

  5. StClowers
    • 10 months ago
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    not sure how to do that..

  6. kropot72
    • 10 months ago
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    You can use a calculator with statistical functions to calculate the sample standard deviation, s.

  7. andijo76
    • 10 months ago
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    x= i got a totally different answer than you did

  8. andijo76
    • 10 months ago
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    and the sd i think is 0.046

  9. StClowers
    • 10 months ago
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    how did you get the sd @andijo76

  10. kropot72
    • 10 months ago
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    @andijo76 what did you get for the sum of the seven data values?

  11. andijo76
    • 10 months ago
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    i found a website back when i was doing pre algebra that helps me figuring out some calculations

  12. andijo76
    • 10 months ago
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    the sum i got was 0.842/7=0.1203

  13. StClowers
    • 10 months ago
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    does anyone know how to input this into the Ti84?

  14. kropot72
    • 10 months ago
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    @andijo76 The correct sum of the seven data values is 0.92.

  15. andijo76
    • 10 months ago
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    im trying to figure out how i got that lol

  16. andijo76
    • 10 months ago
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    is the sd right tho

  17. kropot72
    • 10 months ago
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    My calculator gives the value for the sample standard deviation of s = 0.4634

  18. StClowers
    • 10 months ago
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    @kropot72 how did you input the sd in the calc?

  19. kropot72
    • 10 months ago
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    My calculator is a Casio fx-82 AU PLUS. I just followed the instructions in the User's Guide.

  20. andijo76
    • 10 months ago
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    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
    • 10 months ago
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    there is a website that gives you sd i will paste what it said

  22. andijo76
    • 10 months ago
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    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
    • 10 months ago
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    @andijo76 can you paste the link to the website?

  24. andijo76
    • 10 months ago
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    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
    • 10 months ago
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    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
    • 10 months ago
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    where did you get the 2.576?

  27. kropot72
    • 10 months ago
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    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
    • 10 months ago
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    ok

  29. andijo76
    • 10 months ago
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    i know i am going to sound stupid but how do i figure _g/mi<u<_g/mi was that the answer

  30. kropot72
    • 10 months ago
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    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
    • 10 months ago
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    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
    • 10 months ago
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    so is this the answer then: .0866 g/mi< .1762 g/mi ?! @kropot72

  33. kropot72
    • 10 months ago
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    Looks correct to me :)

  34. andijo76
    • 10 months ago
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    yeah i forgot the point haha

  35. andijo76
    • 10 months ago
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    it amazing how that works hey

  36. kropot72
    • 10 months ago
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    It is a very powerful technique!

  37. andijo76
    • 10 months ago
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    thank you so much for your help

  38. kropot72
    • 10 months ago
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    You're welcome :)

  39. StClowers
    • 10 months ago
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    lol great! thanks!!

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