An article gave the following summary information for fracture strengths (MPa) of n = 196 ceramic bars fired in a particular kiln: x = 55.36

Question

An article gave the following summary information for fracture strengths (MPa) of n = 196 ceramic bars fired in a particular kiln: x = 55.36, s = 3.99. (a) Calculate a (two-sided) confidence interval for true average fracture strength using a confidence level of 95%. (Round your answers to two decimal places.)

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Madeline 2 days 2021-09-15T04:24:56+00:00 1 Answer 0

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    2021-09-15T04:26:36+00:00

    Answer:

    54.80 MPa to 55.92 MPa

    Step-by-step explanation:

    Sample mean fracture strength (x) = 55.36 MPa

    Sample standard deviation (s) = 3.99 MPa

    Sample size (n) = 196.

    The upper and lower bounds for a 95% confidence interval are given by:

    U=x+1.960*\frac{s}{\sqrt{n}} \\L=x-1.960*\frac{s}{\sqrt{n}}

    The upper and lower bounds of the confidence interval are;

    U=55.36+1.960*\frac{3.99}{\sqrt{196}}\\U= 55.92\\L=55.36-1.960*\frac{3.99}{\sqrt{196}}\\L= 54.80\\

    The 95% confidence interval for true average fracture strength is 54.80 MPa to 55.92 MPa

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