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Math Help - Hypothesis question

  1. #1
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    Exclamation Hypothesis question

    Any help is appreciated; I am more or less just trying to figure out if I did this right.

    Also for the question I have:
    -stated the null and alternative hypothesis
    -stated the critical region to reject or fail to reject the null
    -Identified the test stat
    -found the test stat
    -stated the conclusion.

    The question:
    The transit company of a large city bases its fare on the assumption that 30% of riders pay reduced fares. A random sample of 1600 riders showed that 451 of them paid a reduced fare. At the 0.05 level of significance should the transit company continue to base fares on this assumption?

    My answer:
    Ho: p=0.30 H1: p=/=0.30
    Critical region: Reject Ho if the test statisitc does not fall between 1.96 and -1.96. Fail to reject Ho if the test statistic falls between 1.96 and -1.96.
    z=-1.75
    test statistic = 0.0401*2=0.0802

    There is not sufficient evidence to warrant rejection of the claim that 30% of its riders pay reduced fares.
    Yes, the transit company should continue to base fares on this assumption.

    Thanks in advance for you review! It is greatly appreciated.
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  2. #2
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    Quote Originally Posted by Thatgirl View Post
    Any help is appreciated; I am more or less just trying to figure out if I did this right.

    Also for the question I have:
    -stated the null and alternative hypothesis
    -stated the critical region to reject or fail to reject the null
    -Identified the test stat
    -found the test stat
    -stated the conclusion.

    The question:
    The transit company of a large city bases its fare on the assumption that 30% of riders pay reduced fares. A random sample of 1600 riders showed that 451 of them paid a reduced fare. At the 0.05 level of significance should the transit company continue to base fares on this assumption?

    My answer:
    Ho: p=0.30 H1: p=/=0.30
    Critical region: Reject Ho if the test statisitc does not fall between 1.96 and -1.96. Fail to reject Ho if the test statistic falls between 1.96 and -1.96.
    z=-1.75
    test statistic = 0.0401*2=0.0802

    There is not sufficient evidence to warrant rejection of the claim that 30% of its riders pay reduced fares.
    Yes, the transit company should continue to base fares on this assumption.

    Thanks in advance for you review! It is greatly appreciated.
    I don't have time now to type the details, but I get a 95% confidence interval for the proportion of riders who pay reduced fares to be:

    [0.271, 0.293].

    0.30 lies outside this interval so I'd reject.

    I might have time later to find your mistake.
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