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 diamete 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 -0.209 2.429 -0.09 0.929 Diameter 0.7689 0.1471 5.66 0.002 S - 4.07980 R-Sq 88.98 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 = 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? 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.)

Compute the descriptive statistics for the weekly hours spent studying. Describe your findings.

Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made the time period of January 1 to March 31. The table gives the defect and the number of defects. Do the data support the notion that each defect type occurs in the same proportion? Test at the 5% level. Number of Defective Lenses Defect type Number of defects Scratch 1866 Right shaped - small 1935 Flaked 1979 Wrong axis 1921 Chamfer wrong 1864 Crazing, cracks 1991 Wrong shape 2004 Wrong PD 1895 Spots and bubbles 1917 Wrong height 1885 Right shape - big 1875 Lost in lab 1886 Spots/bubble - intern 1935   State the hypotheses.H0: Each defect type     in the same proportion.Ha: Each defect type     in the same proportion. Calculate the χ2 test statistic. Round expected values to two decimal places. Round χ2 to three decimal places.χ2 =  Calculate the p-value. Round to four decimal places.p-value =  State your decision.Since p-value     0.05,…

Doctors are testing a new antidepressant. A group of patients, all with similar characteristics, take part in the study. Some of the patients receive the new drug, while others receive the traditional drug. During the study, a number of patients complain about insomnia. The data are shown in the contingency table below. What is the relative risk of insomnia for those who receive the new drug? Round to two decimal places. New drug Total Insomnia No insomnia Total Traditional drug 36 Provide your answer below: 52 88 226 295 521 278 331 609