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In a manufacturing process, the diameter of the steel rods is the product characteristic. A random sample of 25 steel rods is taken and sample mean is 8.88 cm. The diameter is assumed to be normally distributed with standard deviation 1.25.
(i) Find a 95% confidence interval for the true diameter. If the standard deviation is unknown and the sample standard deviation is 1.25, will the 95% confidence interval be narrower or wider?
(ii) If we would like the difference between the true mean and the sample mean to be less than 0.15, what is the minimum number of steel rods that we need to sample. Use alpha = 0.05.
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