Suppose that if a signal having intensity μ originates at location A, then the intensity recorded at location B is normally distributed with mean μ and standard deviation 3. That is, due to “noise,” the intensity recorded differs from the actual intensity of the signal by an amount that is normal with mean 0 and standard deviation 3. To reduce the error, the same signal is independently recorded 10 times. If the successive recorded values are 17, 21, 20, 18, 19, 22, 20, 21, 16, 19.
(a) (7 pts.) Construct a 95 percent confidence interval for μ, the actual intensity.
(b) (8 pts.) Construct a 90 percent confidence interval for μ