1. A machine produces metal pieces that are cylindrical in shape. A sample of 36 metal...

1. A machine produces metal pieces that are cylindrical in shape. A sample of 36 metal pieces is taken and the mean diameters for this sample was 6.21 centimeters. In addition from previous studies it is know that the population is approximately Normal with a standard deviation 1.84centimeter.

Note: Do the calculations by hand, but show the R code and output for the z-value, t-value or for finding area under the standard normal curve.

Note: Round your numbers to exactly 2 decimal places.

Construct and interpret a 95% confidence interval for the true mean diameter of these metal pieces.
Construct a 99% confidence interval for the true mean diameter of these metal pieces and explain the different in size between the intervals found in (a) and (b)
What do you think would happen to the confidence interval found in (b) if we were to decrease the sample size? Explain.

Expert Solution

orchestra answered 1 year ago

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