A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with

Question

A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0: µ = 12 against H1: µ < 12 using a random sample of n = 4 specimens. Calculate the P-value if the observed statistic is Xbar (average) = 11.25. Suppose that the distribution of the sample mean is approximately normal.

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Thu Cúc 1 year 2021-08-06T15:13:04+00:00 1 Answers 596 views 0

Answers ( )

    1
    2021-08-06T15:14:16+00:00

    Answer:

    The p-value of the test is 0.0013.

    Step-by-step explanation:

    The test statistic is:

    [tex]z = \frac{X – \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

    In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

    12 is tested at the null hypothesis:

    This means that [tex]\mu = 12[/tex]

    Standard deviation of 0.5 kilograms.

    This means that [tex]\sigma = 0.5[/tex]

    Sample of n = 4 specimens. Observed statistic is Xbar (average) = 11.25.  

    This means that [tex]n = 4, X = 11.25[/tex]

    Value of the test statistic:

    [tex]z = \frac{X – \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

    [tex]z = \frac{11.25 – 12}{\frac{0.5}{\sqrt{4}}}[/tex]

    [tex]z = -3[/tex]

    P-value:

    Probability of finding a sample mean belo 11.25, which is the p-value of z = -3.

    Looking at the z-table, z = -3 has a p-value of 0.0013, thus the this is the p-value of the test.

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