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anonymous

  • one year ago

Statistics help!!

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  1. anonymous
    • one year ago
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    For (a):\[P(\hat{p}\ge0.5)=P\left(\frac{\hat{p}-0.3}{0.023}\ge\frac{0.5-0.3}{0.023}\right)\approx P(Z\ge8.696)=\cdots\]The idea here is that you transform the sample proportion to the \(Z\) statistic using \[Z=\frac{\text{sample mean}-\text{population mean}}{\text{sample standard deviation}}\]

  2. anonymous
    • one year ago
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    "The proportion p-hat of the sample..." \(\hat{p}\) is the symbol representing the sample proportion. In this case, it's the proportion of students that report a certain opinion. It's important to know that it's the *sample* proportion because it's the statistic you get from the SRS. It may or may not reflect the *population* proportion. Think of it this way: There are billions of people on the planet. We can't ask every person's opinion on some matter, so we narrow our scope. Instead of asking billions of people the same question, we can simplify the task by asking, say, 10 people. We want to make an inference about *everyone* (the population), but we can't, so we use a manageable fraction of everyone (a sample).

  3. anonymous
    • one year ago
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    The notation \(P(\text{event})\) means the probability of \(\text{event}\) happening, while \(p\) might refer to the population statistic, yes.

  4. anonymous
    • one year ago
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    Actually, you're given all the info about the population: "Suppose that \(\textbf{in fact }\bf{30\%}\textbf{ of all students}\) would never answer drugs if asked this question ... In fact, you can assign probabilities to values of p-hat using the normal density curve with \(\textbf{mean }\bf{0.3}\) and \(\textbf{standard deviation }\bf{0.023}\)." What you're doing here is finding the probability that the sample proportion is greater/less than some value. To find these probabilities, you use the population statistics.

  5. anonymous
    • one year ago
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    To clarify, you're not looking for the actual sample mean - that can only be found by actually collecting data in some experiment or survey. Here, you're just trying to make an inference about what the sample proportion might be based on what you know about the population.

  6. anonymous
    • one year ago
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    You're not finding \(Z\). You're looking for the probability that this \(Z\) is greater/less than something. You can use a \(z\) table like the one here: http://www.statext.com/tables/Z-Table(GreaterThanZ).jpg This table might not be so useful in this case since there's no probability value associated with numbers greater than \(3.99\). You can notice a pattern here, though. As \(z\) increases, the probability trends toward \(0\). Verifying this with W|A: http://www.wolframalpha.com/input/?i=P%28Z%3E%3D8.696%29 As you can see, the probability is very small, near enough to zero to just say zero.

  7. anonymous
    • one year ago
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    Yeah. The same process is used to compute the other probabilities.

  8. jim_thompson5910
    • one year ago
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    you have the correct z score of z = -2.17391 so far so good

  9. jim_thompson5910
    • one year ago
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    do you see how SithsAndGiggles used wolfram alpha to compute the probabilities?

  10. jim_thompson5910
    • one year ago
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    you type in P(Z < -2.17391) into wolfram

  11. jim_thompson5910
    • one year ago
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    http://www.wolframalpha.com/input/?i=+P%28Z+%3C+-2.17391%29

  12. jim_thompson5910
    • one year ago
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    it provides the approximate decimal result along with the drawing (shaded area is very tiny, in blue under the curve)

  13. jim_thompson5910
    • one year ago
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    0.015 if you round to 3 decimal places, but yeah

  14. jim_thompson5910
    • one year ago
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    ok sounds good

  15. jim_thompson5910
    • one year ago
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    what z scores did you get

  16. jim_thompson5910
    • one year ago
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    think of it like this raw score of 0.25 means x = 0.25 z = (x-mu)/sigma z = (x-0.3)/0.023 z = (0.25 - 0.3)/0.023 z = ??

  17. jim_thompson5910
    • one year ago
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    the "mu" is a lot like the population proportion p the "sigma" is the standard deviation of the sample proportions

  18. jim_thompson5910
    • one year ago
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    what z score do you get when you compute z = (0.25 - 0.3)/0.023

  19. jim_thompson5910
    • one year ago
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    good

  20. jim_thompson5910
    • one year ago
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    and when x = 0.35, what is z?

  21. jim_thompson5910
    • one year ago
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    so you'll then type in P( -2.17391 < Z < 2.17391 ) into wolfram alpha

  22. jim_thompson5910
    • one year ago
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    The basic steps are this Step 1) Convert all raw scores to standard z-scores Step 2) Use a program, calculator or table to find the area under the curve. A program like wolfram alpha is probably the easiest since you can type in one line and get the answer directly.

  23. jim_thompson5910
    • one year ago
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    getting the same

  24. jim_thompson5910
    • one year ago
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    so if you randomly picked out a p-hat, there is a 97% chance (roughly) that you'll get a p-hat between 0.25 and 0.35

  25. jim_thompson5910
    • one year ago
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    I'll be on for a bit longer, but I cannot help with the test while you're taking it. That's something that needs to be done on your own. I'm sure you'll do fine on the test. I've found that 50% of it is psychological which means that if you're confident, then you'll most likely do well.

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