Test the hypothesis that the average content of containers of a particular lubricant is 15 liters if the contents of a random sample of 15 c

Question

Test the hypothesis that the average content of containers of a particular lubricant is 15 liters if the contents of a random sample of 15 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, 10.5,11.2,11.3 and 9.8 liters. Use a 0.01 level of significance and assume that the distribution of contents is normal.
Also find 95% confidence interval for the population mean. Interpret your results

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Tài Đức 4 years 2021-08-15T16:15:50+00:00 1 Answers 395 views 0

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  1. thongdat2
    0
    2021-08-15T16:17:15+00:00
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    Answer:

    Kindly check explanation

    Step-by-step explanation:

    Given The samples:

    X = 10.2, 9.7, 10.1, 10.3, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, 10.5,11.2,11.3, 9.8

    Using a calculator ;

    Sample mean, xbar = 10.27

    Sample standard deviation, s = 0.462

    H0 : μ = 15

    H1 : μ < 15

    The test statistic :

    (xbar – μ) ÷ (s/sqrt(n))

    (10.27 – 15) / (0.462/sqrt(15))

    -4.73 / 0.1192878

    = – 39.65

    Using the Pvalue form Tscore, calculator, df = 14

    Pvalue = 0.000001,

    Since, Pvalue < α ; then we reject the Null

    Confidence interval :

    Xbar ± Margin of error

    Margin of Error = Tcritical * s/√n

    TCritical at 95%, df = 14

    Margin of Error = 2.145 * 0.462/sqrt(15) = 0.2559

    Lower boundary :

    10.27 – 0.2559 = 10.0141

    Upper boundary :

    10.27 + 0.2559 = 10.5259

    (10.0141 ; 10.5259)

    The true population means should reside within the interval

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