The household income in a certain city in 2010 had a mean of $48,750 with a standard deviation of $12,200. A random sample of 75 families taken in 2015 produced a mean income of $51,200 (adjusted for...

The household income in a certain city in 2010 had a mean of $48,750 with a standard deviation of $12,200. A random sample of 75 families taken in 2015 produced a mean income of $51,200 (adjusted for inflation).

(a) Assume σ has remained unchanged and test to see whether mean income has changed, using a 0.05 level of significance.

(b) Construct a 90% confidence interval on mean family income in 2015.

(c) Calculate the power of the test if mean income has actually increased to $49,000. Do the same if the mean has increased to $53,000.