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	3380	3390	2300	2480	2620
​28-Day Strength​ (psi), y	5020	5220	4070	4120	4190

(a) Treating the 7-day strength as the explantory variable, x , use technology to determine the estimates of β0 and β1.

β0 ≈b0 = ____ ​(Round to two decimal places as​ needed.)

β1 ≈b1 = ____ (Round to two decimal places as​ needed.)

​(b) Compute the standard error of the estimate , se.

se= ______ ( Rounding to four decimal places)

​(c)  A normal probability plot suggests that the residuals are normally distributed . Use technology to determine sb1 .

Sb1= _____ ( Rounding to four decimal places)

(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 α=0.05 level of significance.

The first step is to set up a hypothesis test. The parameter being tested is the​ slope, β1​, of the linear regression line. If there is no linear relation between the response and explanatory​ variables, the slope of the true regression line will be zero.

The​ P-value for this test is _____ (rounding to three decimal places.)

(e) Use technology to construct a​ 95% confidence interval about the slope of the true​ least-squares regression line.

Lower bound: ____

Upper bound : _____

​(f) What is the estimated mean​ 28-day strength of this concrete if the​ 7-day strength is 3000​ psi?

Y= ______

Answer 1

a) bo=1553.566

b1=1.048

b)se=119.6316

c)sb1=0.1160

d)p value =0.003

e) Lower bound: 0.679

Upper bound =1.417

f)

y=1553.566+1.048*3000 =4697.57 (try 4697.99 if this comes wrong)