A mathematics professor wishes to analyze the relationship between the number of papers (in hundreds) graded by his department's student homework graders and the total amount of money paid to the graders. He collects data for 12 randomly chosen graders and uses MINITAB to do regression analysis. Below is a portion of the MINITAB output. (Here, COST = amount paid, PAPERS = # papers in hundreds, and the intervals listed at the bottom are computed for 1,600 papers.)

The regression equation is

COST = 35.8 + 12.1 PAPERS
Predictor Coef Stdev t-ratio P
Constant 35.80 17.06 2.10 0.062
PAPERS 12.0835 0.9738 12.41 0.000
s = 6.526 R-sq = 93.9% R-sq (adj) = 93.3%
Fit Stdev. Fit 95% C.I. 95% P.I.
229.13 2.34 (223.93 , 234.34) (213.68 , 244.58)

Required:
a. Formulate null and alternative hypotheses about the slope of the true regression line. Adopt the two-sided alternative.
b. What is the least-squares regression equation?
c. What is the standard error about the line (also known as the standard deviation s in the regression model)?
d. What is the slope of the least-squares regression line?
e. The model for regression inference has three parameters: a, b, and s. Estimate these parameters from the data.
f. What is the value of the test statistic for testing the hypotheses?
g. How many degrees of freedom does t have?
h. What is the P-value for the test?
i. Is the number of papers graded useful for predicting the amount paid? Use a significance level of 0.01. Explain briefly.
j. What is the estimated cost of grading 1,600 papers?
k. Find the 95% confidence interval for the average amount paid to all graders who grade 1,600 papers.