In a diagnostic a student correctly answers about 60 of the

In a diagnostic a student correctly answers about 60% of the questions posed. However, after a full semester, there 43 points missed out of a total 150 points attempted; that is, this student answered 107 points correctly. At the 5% level of significance, do these data indicate that the student understands more than he did at the beginning?

Compute the test statistic accurate to two decimals.

Solution

phat=107/150=0.713

The test statistic is
Z=(phat-p)/[p*(1-p)/n]

=(0.713-0.6)/sqrt(0.6*0.4/150)

= 2.83