Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year old baby and the weight y of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females. x (lb) y (lb) 22 128 27 126 25 121 25 20 15 25 21 17 130 130 120 145 130 130 24 130 26 130 22 140 18 110 19 115 In this setting we have x = 306, y = 1785, x = 6864, y = 228,651, and Exy = 39,203. (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your answers for least-squares estimates to four decimal places.) x = y= b= = (b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y). 150 y 150 y 140 130 120 150 140 130 120 y 140 130 120 x 15 20 25 30 15 20 25 30 15 20 25 30 y 150 140 130 120 X 15 20 25 30 (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = , = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) % (d) Test the claim that the population correlation coefficient p is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. OP-value > 0.250 0.125 < P-value < 0.250 O 0.100 < P-value < 0.125 O 0.075 < P-value < 0.100 0.050 < P-value < 0.075 0.025 P-value < 0.050 O 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 0.0005 < P-value < 0.005 OP-value < 0.0005 Conclusion Reject the null hypothesis. There is sufficient evidence that p > 0. Reject the null hypothesis. There is insufficient evidence that p > 0. Fail to reject the null hypothesis. There is sufficient evidence that p > 0. Fail to reject the null hypothesis. There is insufficient evidence that p > 0. (e) If a female baby weighs 15 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) lb (f) Find S. (Round your answer to two decimal places.) Se= (g) Find a 95% confidence interval for weight at age 30 of a female who weighed 15 pounds at 1 year of age. (Round your answers to two decimal places.) lower limit upper limit lb lb (h) Test the claim that the slope of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. OP-value > 0.250 0.125 < P-value < 0.250 O 0.100 P-value < 0.125 O 0.075 < P-value < 0.100 0.050 < P-value < 0.075 0.025 P-value < 0.050 O 0.010 < P-value < 0.025 0.005 < P-value 0. Reject the null hypothesis. There is insufficient evidence that > 0. Fail to reject the null hypothesis. There is sufficient evidence that > 0. Fail to reject the null hypothesis. There is insufficient evidence that > 0. (i) Find an 80% confidence interval for and interpret its meaning. (Round your answers to three decimal places.) lower limit upper limit Interpretation For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval. For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval. For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval. For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval. Dorothy Kelly sells life insurance for the Prudence Insurance Company. She sells insurance by making visits to her clients homes. Dorothy believes that the number of sales should depend, to some degree, on the number of visits made. For the past several years, she kept careful records of the number of visits (x) she made each week and the number of people (y) who bought insurance that week. For a random sample of 15 such weeks, the x and y values follow. x y 13 3 18 12 14 13 28 5 20 14 22 7 15 10 4 8 2 5 6 8 3 5 29 10 8 25 6 10 16 7 In this setting we have x = 247, y = 99, x = 4807, y = 781, and xy = 1837. (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to four decimal places.) x = y = b = = (b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y). 15 10 5 y x 5 10 15 20 25 30 y 15 10 5 5 10 15 20 25 30 15 y 10 15 10 5 10 15 20 25 30 x 5 10 15 20 25 30 (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = 2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) % (d) Test the claim that the population correlation coefficient p is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. P-value > 0.250 0.125 < P-value < 0.250 O 0.100 < P-value 0. Reject the null hypothesis. There is insufficient evidence that p > 0. Fail to reject the null hypothesis. There is sufficient evidence that p > 0. Fail to reject the null hypothesis. There is insufficient evidence that p > 0. (e) In a week during which Dorothy makes 17 visits, how many people do you predict will buy insurance from her? (Round your answer to one decimal place.) people (f) Find Se. (Round your answer to three decimal places.) Se = (g) Find a 95% confidence interval for the number of sales Dorothy would make in a week during which she made 17 visits. (Round your answers to one decimal place.) lower limit upper limit sales sales (h) Test the claim that the slope of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. OP-value> 0.250 0.125 P-value < 0.250 O 0.100 < P-value < 0.125 O 0.075 P-value < 0.100 O 0.050 < P-value < 0.075 0.025 < P-value < 0.050 O 0.010 < P-value < 0.025 O 0.005 P-value < 0.010 O 0.0005 < P-value < 0.005 O P-value < 0.0005 Conclusion Reject the null hypothesis. There is sufficient evidence that > 0. Reject the null hypothesis. There is insufficient evidence that > 0. Fail to reject the null hypothesis. There is sufficient evidence that > 0. Fail to reject the null hypothesis. There is insufficient evidence that > 0. (i) Find an 80% confidence interval for and interpret its meaning. (Round your answers to three decimal places.) lower limit upper limit Interpretation For each additional visit made, sales increase by an amount that falls within the confidence interval. For each less visit made, sales increase by an amount that falls within the confidence interval. For each additional visit made, sales increase by an amount that falls outside the confidence interval. For each less visit made, sales increase by an amount that falls outside the confidence interval.