In order to know whether the average yearly incomes of marketing managers in the East and West of the United States are different in a statistically significant way the following information was gathered. East West n1 = 40 n2 = 45 X1 bar= 80 (in X2 bar = 78 (in $1000) $1000) $1 = 6 (in $1000) $2 = 8 (in $1000) Assuming a level of significance (a) = 0.1 and degrees of freedom = 80, please answer the following questions. 1. State your null and alternate hypotheses: 2. What is the value of the test statistic? Please show all the relevant calculations. 3. What are the rejection criteria based on the critical value approach? 4. What is the Statistical decision (i.e. reject /or do not reject the null hypothesis)? Please also show the justification for your decision