A sample of 56 cotton samples resulted in a sample average percentage elongation of 8.17 and a sample variance of 2.10. Compute a 90% confidence interval for the population average percentage elongation.

( b ) A machine produces metal pieces that are cylindrical in shape. A random sample of 12 metal pieces produced by the machine shows a mean diameter of 1.3 cm and a standard deviation of 0.05 cm. Compute a 98% confidence interval for the true mean diameter for the metal pieces produced by the machine.

( c ) In a random sample of 500 families in a city, it was found that 160 owned plasma TV. Find a 95% confidence interval of the actual proportion of families in the city with plasma TV.