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Math Help - finding hypothesis

  1. #1
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    finding hypothesis

    I had to miss my last 2 calc classes and now i'm completely lost on my homework. I posted two problems, the first i don't even know how to begin to start (i'm really confused as to find the hypothesis) and the second i was able to determine the mean and standard deviation (part a) but after that i'm lost. If anyone is able to offer some step by step assistance i'd really appreciate it.

    A producer of various kinds of batteries has been producing "D" size batteries with a life
    expectancy of 87 hours. Due to an improved production process, management believes that there has
    been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an
    average life of 88.5 hours. Assume from past information that it is known that the standard deviation of
    the population is 9 hours.
    a. Give the null and the alternative hypotheses.
    b. Compute the standardized test statistic.
    c. At 1% (α = .01) significance level test management's belief. State your conclusion


    -----

    The Department of Economic and Community Development (DECD) reported that in 2009 the
    average number of new jobs created per county was 450. The department also provided the following
    information regarding a sample of 5 counties in 2010.
    County New Jobs Created
    In 2010
    Bradley 410
    Rhea 480
    Marion 407
    Grundy 428
    Sequatchie 400
    a. Compute the sample average and the standard deviation for 2010.
    b. We want to determine whether there has been a significant decrease in the average number
    of jobs created. Provide the null and the alternative hypotheses.
    c. Compute the standardized test statistic. Assume the population is normally distributed.
    d. At 5% (α = .05) significance, test the hypotheses. State your conclusion.
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  2. #2
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    Give the null and the alternative hypotheses.
    The precise definition of these should be in your text book. In simple (and therefore approximate) language:

    Null hyopthesis: This is the "baseline" that you are going to compare to. the purpose of the test is to see if there is there is a significant deviation from the expected "baseline" result. If there is a significant deviation, you conclude that the null hypothesis was false.

    eg: Null: Population mean is 10

    Alternative Hypothesis: If the null hypothesis isn't true, then some "alternative" hypothesis must be correct. In a statistical test, the alternative hypothesis specifies the type of deviation from the baseline that you want to test for. This is necessary for technical reasons to decide whether a deviation is significant or not.

    eg: Alternative: Population mean > 10


    Your question
    If i give you the following information, what do you think the "baseline" and "expected deviation" might be? hints in bold.
    A producer of various kinds of batteries has been producing "D" size batteries with a life
    expectancy of 87 hours.
    Due to an improved production process, management believes that there has
    been an increase
    in the life expectancy


    Your issue with the second question seems to be similar. Post your attempt for the rest and say where you are stuck if you need more help.
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  3. #3
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    so H0 = 10, HA = >10?

    is the population mean the same as the standard deviation? (9?)

    cause i'm not too sure where the 10 came from.

    to be completely honest, i really have no idea where i'm going with this. it all sounds like a foreign language to me. if you could just show me how to do the first one i'll probably be able to figure out the second.
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  4. #4
    MHF Contributor
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    10 is a number i made up to give you an example it has nothing to do with your question.

    a)
    define: u = population average battery life
    H0: u=87
    H1: u > 87

    b)



    c)
    the 1% limit for a 1 tailed test is 2.3263

    If z > 2.3263 then reject H0, otherwise do not reject it. I haven't evaluated z so you will need to check.
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  5. #5
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    thank you! i really appreciate it. I think i get it now and should be fine on the second problem. thanks again
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