9. Prehistoric pottery vessels are usually found as sherds (broken pieces) and a
ID: 2909405 • Letter: 9
Question
9. 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.
(a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height?
diameter or height?
(b) For the least-squares line ? = 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.
(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 ? = 0?
H0: ? = 0; H1: ? > 0
H0: ? < 0; H1: ? = 0
H0: ? = 0; H1: ? < 0
H0: ? = 0; H1: ? ? 0
H0: ? ? 0; H1: ? = 0
Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for ? = 0.01?
Reject the null hypothesis. There is sufficient evidence that ? differs from 0.
Fail to reject the null hypothesis. There is insufficient evidence that ? differs from 0.
Fail to reject the null hypothesis. There is sufficient evidence that ? differs from 0.
Reject the null hypothesis. There is insufficient evidence that ? differs from 0.
(d) Recall that the t value and resulting P-value of the slope b equal the t value and resulting P-value of the corresponding correlation coefficient r. To find the value of the sample correlation coefficient r, take the square root of the "R-Sq" value shown in the display. What is the value of r? (Round your answer to three decimal places.)
Consider a two-tailed test for r. Based on the P-value shown in the Minitab display, is the correlation coefficient significant at the 1% level of significance?
No, the correlation coefficient is not significant at the ? = 0.01 level because the P-value ? ?.
Yes, the correlation coefficient is significant at the ? = 0.01 level because the P-value > ?.
Yes, the correlation coefficient is significant at the ? = 0.01 level because the P-value ? ?.
No, the correlation coefficient is not significant at the ? = 0.01 level because the P-value > ?.
S = 4.07980 R-Sq = 72.1% Prehistorkc pottery vessels are usually found as sherds (broken pleces) and are carefully reconstructed f enough sherds can be found. An archaeologkal study provides date relsting x-body diameter in certimeters and y - height in centimeters of preistoric vessels reconstnucted frem sherds found at a prehistork site. The following Minitab printout provides an analysis of the data. (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diemeter of the pot or the height) O diameter Ohelight (b) For the least-squares ine -a+ bx, what is the value of the constant a? What is the value of the slope b? (Note: The slope is the coeficient of the predictor variabile.) Write the equation of the leest-squares ine. The pvgue for ? two-taled test correspondng toeach coemoent is lated under P, The t value corresponding to the coemoent is inted under r. what is the Avalue of the slope? What are the hypotheses for a two tailed test of p 0 Based on the P-value in the printout, do we reject or falil to reject the Nul hypothesis for 001 O Reject the nuil hypothess. There is sufficient evidence that difters from o O Fail to reject the null hypothesis. There is insufficient evidence thet B differs from o Fae to repect the mus hypothesis. There .s sncent evidence that ß diners trom o. Reject the nul hypothesis. There is insuicient evidence that jf differs from o (d) Recal that the t velue and resuling P-yalue of the slope b equal the t velue and resulting P-value of the corresponding cerrelation coeficientr. To find the value of the sample correlation coefficient r, take the square n of the "R-Sq" value shown in the display. What is the value of ? (Round your answer to three decimalplaces
Explanation / Answer
a)as we are predicing eight fom diameter ; therefore diameter is a predictor variable
b)
a =-0.227
b=0.7959
yhat=-0.227+0.7959x
c) P-value of the slope =0.008
H0: ? = 0; H1: ? ? 0
Reject the null hypothesis. There is sufficient evidence that ? differs from 0
d)
value of r =0.849
Yes, the correlation coefficient is significant at the ? = 0.01 level because the P-value ? ?.
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