The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 12 cans yields a sample standard deviation

Question

The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 12 cans yields a sample standard deviation of s = 5.2 milligrams. Calculate the 99% two-sided CI for σ.

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Emery 3 weeks 2021-11-10T15:02:53+00:00 1 Answer 0 views 0

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    2021-11-10T15:04:34+00:00

    Answer:

    3.30185\leq σ \leq 8.7636

    Step-by-step explanation:

    the fromula for 100(1-α)% confidence (two sided) for σ is

    √(η-1)*s^2/x^2_α/2,V \leq σ \leq √(η-1)*s^2/x^2_(1-α/2,V)               ∴ (v=n+1)

    now data given is n = 12 and s=5.2 mg

    for 99% CI ,α=0.05  and (n-1)=9 degree of freedom

    from chi- square table x^2_(0.025,9)=19.02 ; x_(0.975,9)=2.7

    substitute them in above expression we get

    3.30185\leq σ \leq 8.7636

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