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KonradZuse

  • 2 years ago

We wish to see if, on average, traffic is moving at the posted speed limit of 65 miles per hour along a certain stretch of Interstate 70. On each of four randomly selected days, a randomly selected car is timed and the speed of the car is recorded. The observed speeds are 70, 65, 70, and 75 miles per hour. Assuming that speeds are Normally distributed with mean μ, we test whether, on average, traffic is moving at 65 miles per hour by testing the hypotheses H0: μ = 65, Ha: μ ≠ 65.

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  1. KonradZuse
    • 2 years ago
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    Based on the data, the value of the one-sample t statistic is A. 5. B. 4.90. C. 2.45. D. 1.23. Based on these data, A. we would reject H0 at significance level 0.10 but not at 0.05. B. we would reject H0 at significance level 0.05 but not at 0.025. C. we would reject H0 at significance level 0.025 but not at 0.01. D. we would reject H0 at significance level 0.01.

  2. EulerGroupie
    • 2 years ago
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    sample mean is 70, sample standard deviation is 4.08, sample size is 4, degrees of freedom is 3 \[t=\frac{70-65}{\frac{4.08}{\sqrt{4}}}=2.45\]

  3. KonradZuse
    • 2 years ago
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    ic.....

  4. KonradZuse
    • 2 years ago
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    how did we get 4.08 as SD?

  5. EulerGroupie
    • 2 years ago
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    I put the numbers into my TI calculator and calculated all basic stats (I can say more if you have one.) Looking this up in a t table using degrees of freedom 3 with a two tail test gives a p value between 0.05 and 0.025.

  6. KonradZuse
    • 2 years ago
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    hmm ic...

  7. EulerGroupie
    • 2 years ago
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    If the p-value is smaller than the level of significance, then we reject Ho.

  8. KonradZuse
    • 2 years ago
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    that calculator ishax.

  9. KonradZuse
    • 2 years ago
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    it is smaller so we reject it?

  10. EulerGroupie
    • 2 years ago
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    It is smaller than 0.05, but bigger than 0.025... B

  11. KonradZuse
    • 2 years ago
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    but it says reject?

  12. KonradZuse
    • 2 years ago
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    how dfo we know to only do 1?

  13. EulerGroupie
    • 2 years ago
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    yes, reject if p-value<alpha... do not reject if p-value > alpha (alpha is the level of significance)

  14. KonradZuse
    • 2 years ago
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    so we rejected the smaller one I c....

  15. EulerGroupie
    • 2 years ago
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    Usually you know your level of significance before you start... they are making it complicated by saying what if this... now what if this.... now what if.... The idea is that we are looking for: How unusual is it that we get these numbers for our sample if the speed limit is really being obeyed? We say that there is just under a 5 percent chance of getting these numbers if it is obeyed. We reject that claim if the level of significance is higher than that (level of significance is like a rejection level).

  16. KonradZuse
    • 2 years ago
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    b wasn't correct, oh wellsies :(

  17. EulerGroupie
    • 2 years ago
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    The logic is confusing to me... let me look again.

  18. EulerGroupie
    • 2 years ago
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    So you put C for the first one and B for the second?

  19. KonradZuse
    • 2 years ago
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    mhm

  20. EulerGroupie
    • 2 years ago
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    I'm sorry, I don't know why... I've been tutoring this quite a bit lately, and I'm not seeing where I went wrong.

  21. EulerGroupie
    • 2 years ago
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    Wait... I looked up a one tail test... der!

  22. KonradZuse
    • 2 years ago
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    >( :p

  23. EulerGroupie
    • 2 years ago
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    The values from the two tail test are 0.100 and 0.050. It's A. I just looked at the wrong row on the table. I hope that you can still answer.

  24. KonradZuse
    • 2 years ago
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    ok :)

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