Question

As concrete​ cures, it gains strength. The following data represent the​ 7-day and​ 28-day strength in pounds per square inch​ (psi) of a certain type of concrete. Complete parts​ (a) through​ (f) below. ​7-Day Strength​ (psi), x 3340 3380 3330 2300 2480 ​28-Day Strength​ (psi), y 4630 5020 4850 4070 4120 ​(a) Treating the​ 7-day strength as the explanatory​ variable, x, use technology to determine the estimates of beta 0 and beta 1. beta 0almost equalsb 0equals nothing ​(Round to one decimal place as​ needed.) beta 1almost equalsb 1equals nothing ​(Round to four decimal places as​ needed.) ​(b) Compute the standard error of the​ estimate, s Subscript e. s Subscript eequals nothing ​(Round to one decimal place as​ needed.) ​(c) A normal probability plot suggests that the residuals are normally distributed. Determine s Subscript b 1. Use the answer from part ​(b). s Subscript b 1equals nothing   ​(Round to four decimal places as​ needed.) ​(d) A normal probability plot suggests that the residuals are normally distributed. Test whether a linear relation exists between​ 7-day strength and​ 28-day strength at the alphaequals0.05 level of significance. State the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0​: beta 0equals0 Upper H 1​: beta 0greater than0 B. Upper H 0​: beta 1equals0 Upper H 1​: beta 1greater than0 C. Upper H 0​: beta 1equals0 Upper H 1​: beta 1not equals0 D. Upper H 0​: beta 0equals0 Upper H 1​: beta 0not equals0 Determine the​ P-value of this hypothesis test. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) What is the conclusion that can be​ drawn? A. Do not reject Upper H 0 and conclude that a linear relation does not exist between the​ 7-day and​ 28-day strength of a certain type of concrete at the alphaequals0.05 level of significance. B. Reject Upper H 0 and conclude that a linear relation does not exist between the​ 7-day and​ 28-day strength of a certain type of concrete at the alphaequals0.05 level of significance. C. Reject Upper H 0 and conclude that a linear relation exists between the​ 7-day and​ 28-day strength of a certain type of concrete at the alphaequals0.05 level of significance. D. Do not reject Upper H 0 and conclude that a linear relation exists between the​ 7-day and​ 28-day strength of a certain type of concrete at the alphaequals0.05 level of significance. ​(e) Construct a​ 95% confidence interval about the slope of the true​ least-squares regression line. Lower​ bound: nothing ​(Round to three decimal places as​ needed.) Upper​ bound: nothing ​(Round to three decimal places as​ needed.) ​(f) What is the estimated mean​ 28-day strength of this concrete if the​ 7-day strength is 3000​ psi? A good estimate of the mean​ 28-day strength is nothing psi. ​(Round to two decimal places as​ needed.) Click to select your answer(s).

7-Day_Strength_(psi)_-_x   28-Day_Strength_(psi)_-_y
3340   4630
3380   5020
3330   4850
2300   4070
2480   4120

Answer 1