All California schools receive an annual academic performance index (API) that is intended to measure the quality of the school. High scores indicate higher quality. The output shows the results of a regression analysis to predict a school's 2008 API score on the basis of the percentage of students enrolled at that school who receive free or reduced-price meals. The regression is based on a random sample of 50 schools.
a. According to the regression line, what's the mean API score of schools in which no students receive free or reduced-price meals?
b. Interpret the slope in context.
c. State the 95% confidence interval for the slope.
d. A school administrator argues that in California, there is no relationship between the percentage of students who receive free or reduced price meals at a school and that school's API score. Use your confidence interval for the slope to respond to this claim.