New York City (NYC) consists of the five boroughs: Manhattan, Brooklyn, Queens, The Bronx and Staten Island. The US Council estimated in 2009 that the average income in NYC was $640. You were appointed by the US Council to recompute this estimate and investigate the average income of people, who are living in NYC. For that purpose you are asking 50 people from all of the five boroughs about their income. You estimate an average income of $650 with sample standard deviation $145. a) At the 10% significance level, test whether this year's income esti-mate is equal to the US Council estimate from 2009, against the alternative that this year's income estimate is higher than the estimate of the US Council from 2009. Explicitly state the null and alternative hypothesis, compute the ap-propriate test statistic and use the critical value or p-value approach to draw your conclusion. b) Suppose now that the data you have obtained above, were solely drawn by asking people who live in Manhattan, which has the highest average income per capita among all five boroughs. Would you still trust the outcome of the hypothesis test from part (a). Why? Why not? Explain your answer.