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Math Help - Hypothesis 2

  1. #1
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    Hypothesis 2

    Hi
    I need some help with questions from prevous exam..they dont have answers
    can anyone help please?

    Q1. A significance test was performed to test the null hypothesis Ho: μ=2 versus the alternative hypothesis H1: μ≠ 2. The test statistic is z = 1.40. The p-value for this test is approximately
    a.0.08
    b.0.003
    c.0.92
    d.0.70
    e.0.16

    Q2.
    A significance test gives a p-value of 0.04. From this we can:

    a.reject the null hypothesis at the 1% level.
    b.say that the difference between our estimate and the hypothesized value is most likely to be due to sampling variability alone.
    c.reject the null hypothesis test at the 5% level but not at the 1% level
    d.say that the probability that the null hypothesis is false is 0.04
    e.say that the probability that the null hypothesis is true is 0.04

    Q3.
    A 95% confidence interval for the mean (μ) of a random variable, based on the t-distribution, is found to be (4.2, 4.8).
    With minimal further calculations, the p-value for a test of

    Ho :μ=5
    H1 :μ≠ 5

    can be claimed to be :

    a.< 0.05
    b.< 0.001
    c.< 0.01
    d.> 0.05
    e.can't say without knowing the sample size


    Q4.
    A study was undertaken to compare moist and dry storage conditions for their effect on the moisture content(%) of white pine timber. The report on the findings from the study included the following statement:
    "The study showed a significant difference ( observed difference =7.85%-6.75%=1.1%; p-value=0.023) in the moisture content of the pine timber under different storage conditions. Level of Significance (α) for the test was 5%"
    Based on this information, which of one the following statements is necessarily FALSE?

    a. If the researchers used a large enough sample size then even a tiny difference could result in a statistically significant difference
    b. If this study was repeated 100 times over, then we would expect to (incorrectly) conclude there was a difference in the storage methods for approximately 5 of the 100 studies (that is, 5% of the time we would say there was a difference in the storage methods when, in fact, there was none).
    c. A statistically significant difference of 1.1% in the moisture content of the white pine is not necessarily a difference of practical importance
    d. The observed difference between the mean moisture contents (1.1%) is unlikely to be due to chance alone.
    e. The probability that there is no difference between moist and dry storage conditions is 0.023
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  2. #2
    Senior Member MaxJasper's Avatar
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    Re: Hypothesis 2

    Q1 (e)...corrected
    Q2 (c)
    Q3 (a)
    Last edited by MaxJasper; September 12th 2012 at 10:29 AM.
    Thanks from ch5112
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  3. #3
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    Re: Hypothesis 2

    Hi . Thanks for your suggested answer.

    I worked out and it seems to be:

    Q1. e
    Q2. c
    Q3. a
    Q4. e

    am i wrong??
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  4. #4
    Senior Member MaxJasper's Avatar
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    Re: Hypothesis 2

    Q1 (e) is ok
    Thanks from ch5112
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  5. #5
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    Re: Hypothesis 2

    Thanks for you help...can you help me with other 5 questions too??

    Q1.A significance test gives a p-value of 0.04 when testing a null hypothesis. From this we would:
    a.conclude that there is a probability of 0.04 that the null hypothesis is not true;
    b.reject the hypothesis at the 0.05 level;
    c.conclude that there is a probability of 0.04 that the null hypothesis is true;
    d.reject the hypothesis at the 0.01 level;

    For Q1, i found, (c) and (d) is false...but not sure what is exact answer


    Q2. During an angiogram, heart problems can be examined via a small tube (catheter) threaded into the heart from a vein in the patient's leg.
    It is important that the company who manufactures the catheter maintain a diameter of 2.00mm.
    Each day, quality control personnel make several measurements to test H0: μ=2.00 vs H1: μ≠2.00 at a significance level of 0.05.
    If they discover a problem, they will automatically stop the manufacturing process until it is corrected.
    Based on the information provided, which one of the following statements is incorrect?

    a.The quality control personnel will correctly stop the manufacturing process on approximately 95% of occasions when catheters of incorrect diameter are being produced.
    b.A type 2 error in this scenario occurs if the quality control personnel do not stop the process when the mean diameter of the catheters being produced made the catheters useless for threading into a heart vein
    c.The quality control personnel will incorrectly stop the manufacturing process on approximately 5% of occasions when catheters of the right diameter are being produced.
    d.A type 1 error in this scenario occurs when the quality control personnel stop the manufacturing process when, in fact, the mean diameter of the catheters is 2.00 mm.

    For Q2. I found answer is (a)


    Q3. Of the following statements about p-values, which one is FALSE?

    a.The p-value is the probability of observing an effect as extreme, or even more extreme, as the one observed, assuming that the null hypothesis is true.
    b.A small p-value is evidence against the null hypothesis.
    c.The smaller the p-value, the more statistically significant the result.
    d.A large p-value does not prove that the null hypothesis is true.
    e.The p-value is the probability of a type I error.

    For Q3, I found (b),(c) are correct...and not sure which one is really false statement


    Q4. An assumption on which the t-test of μ = μ0 is based, is that:

    a.the significance level is 0.05
    b.the power for μ ≠ μ0 is at least 0.95
    c.the population standard deviation is known
    d.the data variable is normally distributed
    e.the sample size is greater than or equal to 30

    For Q4, the answer should be (d)

    Q5.A significance test was performed to test H0: μ = 2 vs H1: μ ≠ 2 based on a sample of 16 observations.
    The test statistic is t = −2.125. The p-value for this test is in the interval:

    a.(0.1, 1)
    b.(0.05, 0.1)
    c.(0.025, 0.05)
    d.(0.01, 0.025)
    e.(0, 0.01)

    found that, obviously, answer is not: (c) and (d)....then which one is the right answer?
    Last edited by ch5112; September 12th 2012 at 01:46 PM.
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  6. #6
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Hypothesis 2

    Q5 :: P(-2.125|\nu =16-1)=.025307
    Thanks from ch5112
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  7. #7
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    Re: Hypothesis 2

    Hi Max
    Thanks for your help.

    Do you know how to use minitab???
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  8. #8
    Senior Member MaxJasper's Avatar
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    Re: Hypothesis 2

    No, not Minitab
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  9. #9
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    Re: Hypothesis 2

    can you help me with this?
    analyzing the scatter plot
    Thanks....
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  10. #10
    Senior Member MaxJasper's Avatar
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    Re: Hypothesis 2

    1) rhs looks positively correlated to ht for both males & females.
    2) males have larger rhs and ht than females
    3) two females have extra large rhs (outlier)
    4) 1 male small rhs and short (might be Danny DeVito)
    5) males data displays a wider scatter than females
    6) etc etc etc ...
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  11. #11
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    Re: Hypothesis 2

    so.. Does the relationship depend upon gender???
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