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5. [0.3/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.3.005. MY NOTES ASK YOUR TEACHER PR 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 Constant -0.23 2. 42 -0.09 0. 929 Dimnotes D. 7635 0-1471 4.32 0.001 - 4.07980 () Minitab calls the explanatory variable the predictor variable. Which is the predictor variable, the diameter of the pot or the height? O diameter O height (b) For the 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. a =[ b = V = (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 7. What is the P-value of the slope? What are the hypotheses for a two-tailed test of $ = 0? OH : B 0 Based on the P-value in the printout, do we reject or fail to reject the null hypothesis for a = 0.01? Reject the null hypothesis. There is sufficient evidence that B differs from 0. O Fail to reject the null hypothesis. There is insufficient evidence that & differs from 0. O Fail to reject the null hypothesis. There is sufficient evidence that & differs from 0. O 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 : value and resulting P-value of the corresponding correlation coefficient /. 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 ? (Round your answer to three decimal places.)6. [-/1 Points] DETAILS BBUNDERSTAT12 9.3.006. MY NOTES ASK YOUR TEACHER PRACTICE ANOTH Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully 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. Pradiator BE Cont Constant -0.20 2.429 -0.0 D. 923 Dianeter 1.7581 0.1281 3.33 0. 027 3 - 4.20780 R-3q - 85.46 a) The standard error S, of the linear regression model is given in the printout 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 S /VEX" - (1)(Ex). From the Minitab display, what is the value of the standard error for the slope b? (c) The formula for the margin of error E for a co% confidence interval for the slope S can be written as E = t (SE Coef). The Minitab display is based on n = 16 data pairs. Find the critical value t, for a 95% confidence interval in the relevant table. Then find a 95%% confidence interval for the population slope #. (Use 3 decimal places.) lower limit upper limit Need Help? Read It7. [0.1/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.3.008. Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. 0.310 0.286 0.340 0.248 0.367 0.269 2.6 4.0 8.6 3.1 11.1 (a) Verify that Ex = 1.82, Zy = 36.9, Ex? = 0.56205, Ey? = 285.79, Exy = 10.5674, and r = -0.816. Ex Ex ? Ey (b) Use a 10% level of significance to test the claim that p # 0. (Use 2 decimal places.) criticalt Conclusion Reject the null hypothesis, there is sufficient evidence that p differs from 0. Reject the null hypothesis, there is insufficient evidence that p differs from 0. O Fail to reject the null hypothesis, there is insufficient evidence that p differs from 0. O Fail to reject the null hypothesis, there is sufficient evidence that p differs from 0. c) Verify that S # 2.2165, a > 25,158, and b # -62.664. d) Find the predicted percentage y of strikeouts for a player with an x = 0.282 batting average. (Use 2 decimal places.) (e) Find a 90% confidence interval for y when x = 0.282. (Use 2 decimal places.) lower limit upper limit 1% (f) Use a 10% level of significance to test the claim that 8 # 0. (Use 2 decimal places.) critical + + Conclusion Reject the null hypothesis, there is sufficient evidence that & differs from 0. Reject the null hypothesis, there is insufficient evidence that & differs from 0. Fail to reject the null hypothesis, there is insufficient evidence that & differs from 0. O Fail to reject the null hypothesis, there is sufficient evidence that & differs from 0. (g) Find a 90% confidence interval for $ and interpret its meaning. (Use 2 decimal places.) lower limit upper limit8. [0.1/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.3.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. y 2.68 51.3 20.5 0.75 (a) Find Ex, Zy, Ex?, Ey?, Exy, and r. (Round r to three decimal places.) Ex= Ey = 7 2= Exy (b) Use a 19% level of significance to test the claim that p 0. (Use 2 decimal places.) critical Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p > 0 Fail to reject the null hypothesis, there is insufficient evidence that p > 0. Fail to reject the null hypothesis, there is sufficient evidence that p > 0. c) Verify that S # 3.1034, a # -2.190, and b = 6.811. d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x = 3.5. (Use 2 decimal places.) (e) Find a 99% confidence interval for y when x = 3.5. (Use 1 decimal place.) lower limit upper limit (f) Use a 19% level of significance to test the claim that @ > 0. (Use 2 decimal places.) critical t Conclusion Reject the null hypothesis, there is sufficient evidence that 8 > 0. Reject the null hypothesis, there is insufficient evidence that B > 0. Fail to reject the null hypothesis, there is insufficient evidence that B > 0. Fail to reject the null hypothesis, there is sufficient evidence that B > 0. (g) Find a 99% confidence interval for $ and interpret its meaning. (Use 2 decimal places.) ower limit12. [0.89/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.3.015.MI.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the resu the book Ibbotson SBBI published by Morningstar. le from one period to the nex correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see vaccination for 8 weeks. Results are shown in the following time series. A research veterinarian at a major university has developed a new vaccine to protect horses from West Nile virus. An important question is: How predictable is the buildup of antibodies in the horse's blood after the vaccination is given? A large random sample of horses were given the vaccination. The average antibody buildup factor (as determined from blood samples) was measured each week after the Original Time Series Week 2 3 4 5 6 7 Buildup Factor 2.3 4.6 6.2 7.5 8.0 9.4 10.6 12.1 To construct a ser data pairs (x, y) where x original buildup factor data and y = original data shifted ahead by 1 week. This gives us the following data set. Since we are shifting 1 week ahead, we now have 7 data pairs (not 8). Data for Serial Correlation x 2.3 4.6 6.2 7.5 8.0 9.4 10.6 4.6 6.2 7.5 8.0 9.4 10.6 12.1 LO USE SALT For convenience, we are given the following sums. Ex = 48.6, Zy = 58.4, Ex? = 385.86, Ey? = 526.98, Exy = 448.7 (@) Use the sums provided (or a calculator with least-squares regression) to compute the equation of the sample least-squares line, y = a + bx. (Round your answers to four decimal places.) 2 = 8.3429 6= 0.8928