Suppose when a signal having unknown value μ is transmitted from node A, the value received at node B is normally distributed with mean μ and variance 5. In other words, when the signal is sent, then its value received is μ + W where W represents a Gaussian noise with mean 0 and UNKNOWN VARIANCE.
To reduce an error, suppose 16 redundant signals of the same value μ are sent. Upon their receipt at node B, their values were recorded as 2 4 7 3 12 11 5 6 16 14 1 3 9 2 4 1
(a) Construct a 95% confidence interval for μ.
(b) How large must n be so that the confidence interval has a margin of error of 0.2?
(c) There is a filter that can reduce the variance of the noise to 1. If the daily cost of the filter is $1 and the daily cost of each additional redundant signal (above 16) is $0.01, which of the following options is more economical?
• Buy the filter and add redundant signals if needed to achieve a margin of error of 0.2
• Do not buy the filter, but add redundant signals to achieve a margin of error of 0.2