Question

Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. An archaeological study provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data.

Predictor	Coef	SE Coef	T	P
Constant	-0.224	2.429	-0.09	0.929
Diameter	0.7527	0.1471	4.15	0.003
S =  4.07980       R-Sq = 74.2%

(a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height?

diameter

height    

(b) For the least-squares line ŷ = a + bx, what is the value of the constant a? What is the value of the slope b? (Note: The slope is the coefficient of the predictor variable.) Write the equation of the least-squares line.

a =

b =

ŷ = + x

(c) The P-value for a two-tailed test corresponding to each coefficient is listed under P. The t value corresponding to the coefficient is listed under T. What is the P-value of the slope?


What are the hypotheses for a two-tailed test of β = 0?

H₀: β < 0; H₁: β = 0

H₀: β ≠ 0; H₁: β = 0   

H₀: β = 0; H₁: β < 0

H₀: β = 0; H₁: β ≠ 0

H₀: β = 0; H₁: β > 0

Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for α = 0.01?

Reject the null hypothesis. There is sufficient evidence that β differs from 0.

Fail to reject the null hypothesis. There is insufficient evidence that β differs from 0.  

Fail to reject the null hypothesis. There is sufficient evidence that β differs from 0.

Reject the null hypothesis. There is insufficient evidence that β differs from 0.

Answer 1

Answer:

Given,

Predictor	Coef	SE Coef	T	P
Constant	-0.224	2.429	-0.09	0.929
Diameter	0.7527	0.1471	4.15	0.003

S =  4.07980       R-Sq = 74.2%

a) diameter

b) a = -0.224, b = 0.7527,

y^ = - 0.224 + 0.7527*x

c) P-value for slope = 0.003

The hypotheses for a two-tailed test of β = 0 is  

H0: β = 0; H1: β ≠ 0

Reject the null hypothesis.

There is sufficient evidence that β differs from 0.

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