Question

u LLS FRUICHUISJ and 6 use the following information. Prehistoric pottery vessels are usually found as sherds (broken pieces) and are care- fully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A.J. McIntyre (University of New Mexico Press) 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 Constant -0.223 2.429 0.7848 0.1471 S = 4.07980 R-SQ = 80.38 -0.09 5.33 0.929 0.001 5. Critical Thinking: Using Information from a Computer Display to Test for Significance Refer to the Minitab printout regarding prehistoric pottery. (a) Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? e least-squares line y = 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 ed under "P." Thet 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 B = 0? Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for a = 0.01? (d) Recall that the I value and resulting P-value of the slope b equal the value and resulting P-value of the corresponding sample 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? Consider a two-tailed test for p. Based on the P-value shown in the Minitab display, is the correlation coefficient significant at the 1% level of significance? 6. Critical Thinking: Using Information from a Computer Display to Find a Confidence interval Refer to the Minitab printout regarding prehistoric pottery. (a) The standard error S of the linear regression model is given in the print- out as "S." What is the value of S? (b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for b is From the Minitab display, what is the value of the standard error for the

Answer 1

(a)
The predictor variable is the diameter.

(b)
The value of a is -0.223
The value of b is 0.7848

The equation of least squares line is,
y = -0.223 + 0.7848 x

(c)
P-value of the slope is 0.001
The hypotheses are,

Ho:B=0

H:8 +0

Since p-value is less than 0.01 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that

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(d)

r = = 0.8961

V0.803

P-value of the correlation coefficient is 0.001
Since p-value is less than 0.01 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that correlation coefficient is not 0 at 1% level of significance.