Question

In: Statistics and Probability

Do cash incentives improve learning? A high-school teacher in a low-income urban school in Worcester, Massachusetts,...

Do cash incentives improve learning? A high-school teacher in a low-income urban school in Worcester, Massachusetts, used cash incentives to encourage student learning in his AP Statistics class. In 2010, 15 of the 80 students enrolled in his class scored a 5 on the AP Statistics exam. Worldwide, the proportion of students who scored a 5 in 2010 was 0.15. Is this evidence that the proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is higher than the worldwide proportion of 0.15?

Conduct a hypothesis test at the significance level α = 0.05 to determine if evidence is present regarding the use of cash incentives to motivate AP Statistics students to do better on their AP exams.

Expert Solution

we want to test that the proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is higher than the worldwide proportion of 0.15.

Ho:- P = 0.15 vs Ha:- P > 0.15

ie. Ho:- The proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is not higher than the worldwide proportion of 0.15.

Vs

Ha:- The proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is higher than the worldwide proportion of 0.15.

In 2010, 15 of the 80 students enrolled in his class scored a 5 on the AP Statistics exam.

n = total number of students enrolled = 80

x= number of students scored 5 = 15

p= proportion of students scored 5 out of 80 = x/n = 15/80 = 0.1875

the significance level α = 0.05

P-value = P( Z > Zcal )

= P( Z > 0.939 )

= 0.1378 ........from normal distribution

Reject Ho if P-value < alpha

P-value = 0.1378 > α = 0.05

We fail to reject Ho at 5% l.O.S

We may conclude that there is No sufficient evidence that the proportion of students who would score a 5 on the AP Statistics exam when taught by the teacher in Worcester using cash incentives is higher than the worldwide proportion of 0.15.

orchestra answered 2 years ago

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