# Question

A process produces cable for the local telephone company. When the process is operating correctly, cable diameter follows a normal distribution with mean 1.6 inches and standard deviation 0.05 inch. A random sample of 16 pieces of cable found diameters with a sample mean of 1.615 inches and a sample standard deviation of 0.086 inch.

a. Assuming that the population standard deviation is 0.05 inch, test, at the 10% level against a two-sided alternative, the null hypothesis that the population mean is 1.6 inches. Find also the lowest level of significance at which this null hypothesis can be rejected against the two-sided alternative.

b. Test, at the 10% level, the null hypothesis that the population standard deviation is 0.05 inch against the alternative that it is bigger.

a. Assuming that the population standard deviation is 0.05 inch, test, at the 10% level against a two-sided alternative, the null hypothesis that the population mean is 1.6 inches. Find also the lowest level of significance at which this null hypothesis can be rejected against the two-sided alternative.

b. Test, at the 10% level, the null hypothesis that the population standard deviation is 0.05 inch against the alternative that it is bigger.

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