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KonradZuse Group Title

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.

  • one year ago
  • one year ago

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  1. KonradZuse Group Title
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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.

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

    • one year ago
  3. KonradZuse Group Title
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    ic.....

    • one year ago
  4. KonradZuse Group Title
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    how did we get 4.08 as SD?

    • one year ago
  5. EulerGroupie Group Title
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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.

    • one year ago
  6. KonradZuse Group Title
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    hmm ic...

    • one year ago
  7. EulerGroupie Group Title
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    If the p-value is smaller than the level of significance, then we reject Ho.

    • one year ago
  8. KonradZuse Group Title
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    that calculator ishax.

    • one year ago
  9. KonradZuse Group Title
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    it is smaller so we reject it?

    • one year ago
  10. EulerGroupie Group Title
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    It is smaller than 0.05, but bigger than 0.025... B

    • one year ago
  11. KonradZuse Group Title
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    but it says reject?

    • one year ago
  12. KonradZuse Group Title
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    how dfo we know to only do 1?

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

    • one year ago
  14. KonradZuse Group Title
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    so we rejected the smaller one I c....

    • one year ago
  15. EulerGroupie Group Title
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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).

    • one year ago
  16. KonradZuse Group Title
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    b wasn't correct, oh wellsies :(

    • one year ago
  17. EulerGroupie Group Title
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    The logic is confusing to me... let me look again.

    • one year ago
  18. EulerGroupie Group Title
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    So you put C for the first one and B for the second?

    • one year ago
  19. KonradZuse Group Title
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    mhm

    • one year ago
  20. EulerGroupie Group Title
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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.

    • one year ago
  21. EulerGroupie Group Title
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    Wait... I looked up a one tail test... der!

    • one year ago
  22. KonradZuse Group Title
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    >( :p

    • one year ago
  23. EulerGroupie Group Title
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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.

    • one year ago
  24. KonradZuse Group Title
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    ok :)

    • one year ago
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