In order to know whether there is a significant difference between the average yearly incomes of marketing managers in the East and West of the United States, the following information was gathered.

East: n₁ = 30; x₁ = 82 (in $1000); s₁ = 6 (in $1000)

West: n₂ = 30; x₂= 78 (in $1000); s₂ = 6 (in $1000)

1. State your null and alternative 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? Use = 0.05 and degrees of freedom = 58.
4. What is the Statistical decision (i.e., reject /or do not reject the null hypothesis)? Justify your answer.