Question

The Academic Performance Index (API) is a measure of school achievement, with scores ranging from 200 to 1000. The API was measured for 8 different schools based on the percent of students at each school who are considered "English Learners" (EL). Use the table below to answser the following questions.

	Estimate	Std. Error	t
Intercept	844.935	18.656	45.290
EL	-1.745	0.415	-4.205

a) Write down the least squares line based on the information given above

y hat = ______ + _____x

b) Is there evidence to support a negative linear relationship between API and the percent of EL? Test using ? = 0.01.

?0: ? =, <, >, /= 0

H_A: ? ? =, <, >, /= 0

Test Statistic: t = ______
Critical value: ?? = ______

Decision: Reject/Fail to Reject

Interpretation: There is/isn't evidence to support a negative linear relationship between API and the percent of EL.

c) Find the 99% confidence interval for ?.
b = _____
??/2 = _____
SE = _____
(____ ,_____ )

Answer 1

a) Write down the least-squares line based on the information given above

y hat = 844.935 + -1.745 x

b) ?0: ? = 0

HA: ? < 0

Test Statistic: t =-4.205
Critical value: ?? = -3.14

Decision: Reject Ho

Interpretation: There is evidence to support a negative linear relationship between API and the percent of EL.

c) Find the 99% confidence interval for ?.
b =-1.745
??/2 = 3.71
SE = 0.415

99% confidence interval for ?
(-1.745-3.71*0.415 ,(-1.745+3.71*0.415 ) =(-1.745-1.540 ,(-1.745+1.540) =( -3.285,-0.205)