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.

Listed below are time intervals (min) between eruptions of a geyser. assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. do not assume that the population standard deviations are equal. does it appear that the mean time interval has changed? is the conclusion affected by whether the significance level is 0.10 or 0.01? recent 78 90 90 79 57 101 62 87 71 87 81 84 57 80 74 103 62 past 88 89 93 94 65 85 85 92 87 91 89 91 follow the steps of hypothesis testing, including identifying the alternative and null hypothesis, calculating the test statistic, finding the p-value, and making a conclusions about the null hypothesis and a final conclusion that addresses the original claim. use a significance level of 0.10. is the conclusion affected by whether the significance level is 0.10 or 0.01? answer choices below: a) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.01 but is not rejected when the significance level is 0.10. b) no, the conclusion is not affected by the significance level because h0 is not rejected regardless of whether a significance level of 0.10 or 0.01 is used. c) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.10 but is not rejected when the significance level is 0.01. d) no, the conclusion is not affected by the significance level because h0 is rejected regardless of whether a significance level of 0.10 or 0.01 is used.