Question

Historically, the standard deviation for the concentricity of an engine oil seal groove is 0.75. The...

  1. Historically, the standard deviation for the concentricity of an engine oil seal groove is 0.75. The target average concentricity is 13.5. A random sample of size 25 was taken, and the sample mean was found to be 13.8. Researchers wonder if this is evidence to conclude that the true mean concentricity has changed. Suppose the concentricity of an engine oil seal groove follows a normal distribution.
    1. Construct a 95% confidence interval for the true mean concentricity. Show work below.
    2. What sample size, n, would be required to obtain a 95% confidence interval for the true mean concentricity with a width of ±0.2? Show work below.
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Answer #1

Here using ti-83 calculator for confidence interval.

a)

95% confidence interval for the true mean

concentricity is 13.506 to 14.094

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