A politician claimed that household income has actually increased from the previously recorded average of $60,000/year in some region in the country. Assuming a (60000, 3000^2) distribution under the null hypothesis of no change in household income, what is the power of the one-sided test ( = 0.05) to detect that the household income has increased by $1000?

Make computations in terms of a normal distribution and assume the sample size is = 50. Hint: Begin by establishing a decision rule in terms of ;. Then determine the probability that ;would cause the null hypothesis to be rejected if the specific alternative value is true.