Prehistoric pottery vessels are usually found as sherds (broken pieces) and are
ID: 3051275 • Letter: P
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. SE Coe -0.209 2-429 -0.09 0.929 07770 -147 5-4-07980 R-Sq 72.1% “ (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? diameter O height (b) For the least-squares line a + bx, w hat 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? 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 i$ sufficient evidence that differs from 0. O 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, te correlation coefficient is not significant at the -0.01 level because the P-values cz. Yes, the correlation coefficient is significant at the . 0.01 level because the Avalue > a. Yes, the correlation coefficient is significant at the 0.01 level because the Avalue a. O No, the correlation coefficient is not significant at the . 0.01 level because the P-value > .Explanation / Answer
(a) Correct answre: Option (A) Diameter
(b) a = -0.209
b = 0.7770
Y-hat = -0.209 + 0.7770 Diameter
(c) P-value of Slope = 0.008
Correct answer: Option (B) H0: beta = 0 H1: beta not = 0
Correct Answer: Option (A) Reject the nully hypothesis. There is sufficient eveidence that beta different from 0
(d) r = sqrt(0.721) = 0.84912
Correct answer: Option (C)