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Math Help - Econometrics

  1. #1
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    Econometrics

    Hi there. Some help solving an econometrics task would be greatly appreciated. I don't get around very well in the field of econometrics and I most certainly don't know Excel functions.

    So, the task is as follows.
    A manufacturer of batteries has previously identified that the average battery life is 299 hours. The producer is now interested in checking, whether the average battery life has expanded with technological advancements.
    For that, 200 batteries were randomly chosen and tested. The average battery life was 300 hours with a standard deviation of 8 hours.
    Control the hypethesis at a significance level of 5%.

    The initial data, as I see it:
    H0: μ<=299
    H1: μ>299
    α= 0.05
    X= 300
    s= 8

    I'm correct so far, how do I proceed from here? Obviously it's a one-tailed test. But function do I use to determine the critical value? And how to find the upper confidence level?

    Again, any help would be hugely appreciated.
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  2. #2
    MHF Contributor

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    Re: Econometrics

    Obviously, "300 hours" is greater then "299 hours". The question is whether that could have happened by chance. I see no reason not to use the standard Normal distribution with mean 299 and standard deviation 8. Then 300 hours cooresponds to a "z" parameter of (300- 299)/8= 1/8. What is the probability that a standard normal z is between 0 and 1/8?
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  3. #3
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    Re: Econometrics

    Wait, so using the t-test wouldn't be correct?
    As I initially computed the test statistic (300-299)/(8/√200))=1.767...
    And since the critical value in a one-tailed test is 1.652..., I came to the conclusion that the null hypothesis should be rejected because t stat > t critical.
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