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.

7-Day_Strength_(psi)_-_x   28-Day_Strength_(psi)_-_y
2300   4070
3380   5020
2620   4190
3390   5220
3330   4850

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

β0≈b0=1753.9 ​

(Round to one decimal place as​ needed.)

β1≈b1=0.9707

​ (Round to four decimal places as​ needed.)

Se=150.6

​(Round to one decimal place as​ needed.)

​(c) A normal probability plot suggests that the residuals are normally distributed. Determine sb1. Use the answer from part (b).

sb1=0.1477

(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 α=0.05 level of significance. State the null and alternative hypotheses. Choose the correct answer below.

A. H0​: β1=0 H1​: β1≠0

Determine the​ P-value of this hypothesis test.

​P-value=0.007

​(Round to three decimal places as​ needed.)

What is the conclusion that can be​ drawn?

A.

Do not reject H0 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 α=0.05 level of significance.

B.

Do not reject H0 and conclude that a linear relation exists between the​ 7-day and​ 28-day strength of a certain type of concrete at the α=0.05level of significance.

C.

Reject H0 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 α=0.05 level of significance.

D.

Reject H0 and conclude that a linear relation exists between the​ 7-day and​ 28-day strength of a certain type of concrete at the α=0.05 level of significance.

Answer 1

here as you can clearly see the results in above image so answers are as follows:

a) β0=b0= 1753.89066

β1=b1= 0.9707

Se= 150.6

c) sb1= 0.1476

d) H0: slope is equal to zero i.e. β1=0 vs

H1: slopesis not equal to zero i.e. β1​​​​​​ not equal to 0

From the third table we get the value p= 0.007

So here p < 0.05

We Reject H0 and conclude that a linear relation exists between the​ 7-day and​ 28-day strength of a certain type of concrete at the α=0.05 level of significance.