Question

Financial incentives for college students. A study reported in Inside Higher Education News (May 22, 2006) found that financial incentives can improve low-income college students’ grades and retention. As part of their “Opening Doors” program, a Louisiana community college offered to pay students $1,000 per semester on the condition that they maintain at least half-time enrollment and at least a 2.0 grade point average (GPA).

a. About 61% of Opening Doors students enrolled full time as opposed to about 52% of traditional students. Identify the target parameter for this comparison.

Short answer

a. The target parameter of the comparison is\(\left( {{{\hat p}_1} - {{\hat p}_2}} \right).\)

Step-by-step solution

Given information.

Financial incentives can improve low-income college student’s grades and retention.

The community college offered to pay $1000 per semester on condition that they maintain at least half-time enrollment and at least a GPA of 2.0.

State the condition required for valid large sample inference about \(\left( {{{\hat p}_1} - {{\hat p}_2}} \right).\)                                                               \(\)

The condition required for valid large sample inference is given as follows:

• The two samples are randomly selected in an independent manner from the two target populations.
• The sample sizes \({n_1}\)and \({n_2}\)are both large so that the sampling distribution of \(\left( {{{\hat p}_1} - {{\hat p}_2}} \right)\) will be approximately normal.

Identify the target parameter of this comparison

The comparison is that about 61% of Opening Doors students enrolled full-time as opposed to about 52% of traditional students.

According to the information of the comparison, \({\hat p_1}\)is the proportion of opening door students enrolled and \({\hat p_2}\) is the proportion of traditional students enrolled.

The proportion of opening door students enrolled is 61%.

\(\begin{aligned}{c}{{\hat p}_1} &= \frac{{61}}{{100}}\\ &= 0.61\end{aligned}\)

The proportion of traditional students enrolled is 52%.

\(\begin{aligned}{c}{{\hat p}_2} &= \frac{{52}}{{100}}\\ &= 0.52\end{aligned}\)

As we know that to compare two proportions, we need to consider the difference of population proportions. So, the target parameter is the difference of population proportions,\(\left( {{{\hat p}_1} - {{\hat p}_2}} \right)\).

Hence, the target parameter of the comparison is \(\left( {{{\hat p}_1} - {{\hat p}_2}} \right).\)