Question

The American Economic Review published a study on whether the removal of credit constraints would impact the likelihood of a student dropping out of college. As part of the investigation, the researchers looked for factors other than credit constraints that would influence the college dropout decision. One factor of interest was expected GPA for a college student who studies 3 hours per day. In a representative sample of 307 college students, the researchers reported the following summary statistics of the expected GAP of those who studies 3 hours per day:

a.       Give an interval that will contain at least 99.7% of the 307 GPAs.

b.       If observe a GPA of 1.40, is it likely that this college student studies 3 hours per day? Explain

Answer 1

Result:

The American Economic Review published a study on whether the removal of credit constraints would impact the likelihood of a student dropping out of college. As part of the investigation, the researchers looked for factors other than credit constraints that would influence the college dropout decision. One factor of interest was expected GPA for a college student who studies 3 hours per day. In a representative sample of 307 college students, the researchers reported the following summary statistics of the expected GAP of those who studies 3 hours per day:

Mean = 3.11, sd=0.66

a.       Give an interval that will contain at least 99.7% of the 307 GPAs.

3 standard limit contain at least 99.7%mof the data

The required interval = (3.11-3*0.66, 3.11+3*0.66)

= (1.13, 5.09 )

b.       If observe a GPA of 1.40, is it likely that this college student studies 3 hours per day? Explain

Since the interval (1.13, 5.09 ) contains 1.40, it is likely that this college student studies 3 hours per day.