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      3330     2480     2620    3380     2300

28-Day Strength (psi), y    4850     4120     4190    5020     4070

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

β0 ≈ b0 =_________(Round to one decimal place as needed.)

β1 ≈ b1 =__________(Round to one decimal place as needed.)

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

se =_________ (Round to one decimal place as needed.)

(c) A normal probability plot suggests that the residuals are normally distributed. Determine s_b1. Use the answer from part (b).

s_{b1=_______________}(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

B. H0 : β1 = 0

      H1 : β1 > 0

C. H0 : β0 = 0

     H1 : β0 ≠ 0

D. H0 : β0 = 0

     H1 : β0 > 0

Determine the P-value of this hypothesis test.

  P-value =_________ (Round to three decimal places as needed.)

What is the conclusion that can be drawn?

A. 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.

B. 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.

C. 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 = 0.05 level of significance.

D. 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.

(e) Construct a 95% confidence interval about the slope of the true least-squares regression line. Lower bound:___________(Round to three decimal places as needed.)

Upper bound: __________(Round to three decimal places as needed.)

(f) \/Vhat 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 _______psi. (Round to tvvo decimal places as needed.)

Answer 1

a)

bo=2014.8

b1=0.9

b)se=95.9

c) Sb1=0.0935

d)

A. H0 : β1 = 0

      H1 : β1 ≠ 0

P-value = 0.003

A. 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.

e)

Lower bound: =0.562

Upper bound: =1.157

f)

A good estimate of the mean 28-day strength is 2038.91 ( please try 2040.00 if this comes wrong)