** A random sample of 21 nickels measured with a very accurate micrometer showed a mean diameter of 0.834343 inches with a standard deviation of 0.001886 inches. (a) Why would nickel diameters vary? (b) Construct a 99 percent confidence interval for the true mean diameter of a nickel. (c) Discuss any assumptions that are needed. (d) What sample size would ensure an error of 0.0005 inches with 99 percent confidence? (Data are from a project by MBA student Bob Tindall.)**

**NBC asked a sample of VCR owners to record Late Night with David Letterman on their VCRs. Of the 125 VCR owners surveyed, 83 either gave up or screwed up because they did not understand how to program the VCR. (a) Construct a 90 percent confidence interval for the true proportion of VCR owners who cannot program their VCRs. (b) Would viewers of this program be typical of all television viewers? Explain. (Data are from Popular Science 237, no. 5, p. 63.)**