Ferric chloride is used as a flux in some types of extraction metallurgy process

Question

Ferric chloride is used as a flux in some types of extraction metallurgy processes. This material is shipped in containers, and the container weight varies. It is important to obtain an accurate estimate of mean container weight. Suppose that from long experience a reliable value for the standard deviation of flux container weight is determined to be 4 lb. How large a sample would be required to construct a 95% two-sided confidence interval on the mean that has a total width of 1 lb? The output voltage of a power supply is assumed to be normally distributed. Sixteen observations taken at random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 9.25, 9.38, and 10.85. Test the hypothesis that the mean voltage equals 12 V against a two-sided alternative using alpha = 0.05. Construct a 95% two-sided confidence interval on mu. Test the hypothesis that sigma^2 = 11 using infinity = 0.05. (d) Construct a 95% two-sided confidence interval on sigma. Construct a 95% upper confidence interval on sigma. Does the assumption of normality seem reasonable for the output voltage?

Explanation / Answer

1. Here z=1.96 and sd=4

Also E=1

Formula for E=z*sd/sqrt(n)

So n=(z*sd/E)^2=61.4656=61

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