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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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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:

[tex]U=x+1.960*\frac{s}{\sqrt{n}} \\L=x-1.960*\frac{s}{\sqrt{n}}[/tex]

The upper and lower bounds of the confidence interval are;

[tex]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\\[/tex]

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

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