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5 November, 02:43

1A technical magazine stated that the mean retail cost of all models of a particular laptop was $600. A random sample of 10 stores that sell that laptop in Los Angeles found it sold with a mean cost of $ 586.50 and a standard deviation of $26.77. Does this indicate that the mean cost of that laptop in Los Angeles is less than $ 600

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  1. 5 November, 02:53
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    Yes

    Step-by-step explanation:

    Given,

    Population mean Z = 600

    Sample mean, µ = 586.50

    Size of the sample, n = 10

    Standard deviation, σ = 26.77

    The testing hypothesis is,

    Null hypothesis = µ<600

    Alternative hypothesis = µ≥600

    The test statistics is the calculated value of Z,

    (Z - µ) / (σ/√n)

    = (600-586.50) / (26.77/√10)

    = (13.5*3.1623) / 26.77

    = 42.691/26.77

    = 1.5947

    And at 5% level of significance, the table value of Z = 1.644

    Here, calculated Z
    So, the null hypothesis is accepted. The mean value of the laptop is less than 600.
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