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Math Help - Small Sample Inferences About a Single Mean

  1. #1
    Super Member Aryth's Avatar
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    Small Sample Inferences About a Single Mean

    Long Lasting Lighting Company has developed a new headlamp for automobiles. The high intensity lamp is expensive but has a lifetime that the company claims to be greater than that of the standard lamp used in automobiles. The standard has an average lifetime equal to 2500 hours. The company wishes to use a small sample to test H_0: \mu = 2500 hours versus the research hypothesis H_a: \mu > 2500 hours at \alpha = 0.05. The company uses a small sample because the lamps are expensive and they are destroyed in the testing process. The lifetimes are determined by using the lamps until they expire. The lifetimes of the 15 randomly selected lamps are:

    3161
    3150
    3134
    3124
    3033
    2959
    2862
    2860
    2843
    2827
    2669
    2575
    2570
    2423
    2364
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  2. #2
    Senior Member
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    Quote Originally Posted by Aryth View Post
    Long Lasting Lighting Company has developed a new headlamp for automobiles. The high intensity lamp is expensive but has a lifetime that the company claims to be greater than that of the standard lamp used in automobiles. The standard has an average lifetime equal to 2500 hours. The company wishes to use a small sample to test H_0: \mu = 2500 hours versus the research hypothesis H_a: \mu > 2500 hours at \alpha = 0.05. The company uses a small sample because the lamps are expensive and they are destroyed in the testing process. The lifetimes are determined by using the lamps until they expire. The lifetimes of the 15 randomly selected lamps are:

    3161
    3150
    3134
    3124
    3033
    2959
    2862
    2860
    2843
    2827
    2669
    2575
    2570
    2423
    2364
    You need to begin by computing the sample S mean E(X) and standard deviation s:

    E(X)=\frac{1}{n}\sum{S}

    s=\sqrt{E(X^2)-[E(X)]^2}

    That should get you started.
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