The diameter of cork of a Champagne bottle is supposed to be 1.5 cm. If the cork is either too large or too small, it will not fit in the bo

Question

The diameter of cork of a Champagne bottle is supposed to be 1.5 cm. If the cork is either too large or too small, it will not fit in the bottle. The manufacturer measures the diameter in a random sample of 36 bottles and finds their mean diameter to be 1.4 cm with standard deviation of 0.5 cm. Is there evidence at 1% level that the true mean diameter has moved away from the target?

in progress 0
Hưng Khoa 4 years 2021-07-24T04:19:56+00:00 1 Answers 22 views 0

Answers ( )

  1. phucdien
    0
    2021-07-24T04:21:05+00:00
    Reply

    Answer:

    t_{n-1,\alpha/2}=3.59114678

    Therefore we do not have sufficient evidence at 1\% level that the true mean diameter has moved away from the target

    Step-by-step explanation:

    From the question we are told that:

    Sample size n=36

    Mean diameter \=x=1.4

    Standard deviation \sigma=0.5cm

    Null hypothesis H_0 \mu=1.5

    Alternative hypothesis \mu \neq 1.5

    Significance level 1\%=0.001

    Generally the equation for test statistics is mathematically given by

    t=\frac{\=x-\mu}{\frac{s}{\sqrt{n} } }

    t=\frac{1.4-1.5}{\frac{0.5}{\sqrt{36} } }

    t=-1.2

    Therefore since this is a two tailed test

    t_{n-1,\alpha/2}

     Where

       n-1=36-1=>35

       \alpha=/2=0.001/2=>0.0005

    From table

    t_{n-1,\alpha/2}=3.59114678

    Therefore we do not have sufficient evidence at 1\% level that the true mean diameter has moved away from the target

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )