. A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine th

Question

. A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses salad dressings is working properly when 8 ounces are dispensed. Suppose that the average amount dispensed in a particular sample of 35 bottles is 7.91 ounces with a variance of 0.03 ounces squared. Is there evidence that the machine should be stopped and production wait for repairs

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Thu Thủy 2 months 2021-08-25T16:56:43+00:00 1 Answers 36 views 0

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    2021-08-25T16:57:55+00:00

    Answer:

    The calculated value |t| = |-3.082| =3.082 > 2.0322 at 0.05 level of significance

    The null hypothesis is rejected

    An alternative hypothesis is accepted

    There is evidence that the machine should be stopped and production wait for repairs

    Step-by-step explanation:

    Step(i):-

    Given that the mean of the Population(μ) = 8 ounces

    Given that the sample size ‘n’ = 35

    The mean of the sample(x⁻) = 7.91

    The variance of the sample  S² = 0.03 ounces

                                               S = √0.03 =  0.1732

    Step(ii):-

    Null Hypothesis: H₀: There is no evidence that the machine should be stopped and production wait for repairs

    Alternative Hypothesis: H₁: There is evidence that the machine should be stopped and production wait for repairs

    t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }

    t = \frac{7.91 -8}{\frac{0.1732}{\sqrt{35} } }

    t = – 3.082

    |t| = |-3.082| =3.082

    Degrees of freedom

    ν = n-1 = 35-1=34

    t₀.₀₅ =  2.0322

    The calculated value |t| = |-3.082| =3.082 > 2.0322 at 0.05 level of significance

    The null hypothesis is rejected

    An alternative hypothesis is accepted

    conclusion:-

    There is evidence that the machine should be stopped and production wait for repairs

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