Suppose a study has been conducted to determine whether there is a difference between student debt at private, for-profit universities and public universities. It was found from random samples that the private, for-profit colleges' average debt was $38,300 and the public colleges average was $11,800. The respective standard deviations were $2,050 and $2,084. The sample sizes were 75 and 205, respectively. Conduct a hypothesis test to determine if there is significance difference between the private, for-profit universities and public universities (Use a 0.05 significance level).