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Using Correct Distribution. In Exercises 5–8, assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) Find the critical value tα/2, (b) find the critical value zα/2 or (c) state that neither the
7. Denver Bronco Salaries Confidence level is 99%, σ = 3342 thousand dollars, and the histogram of 61 player salaries (thousands of dollars) is shown in Exercise 6.
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- Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 15.8 18.1 14.4 19.6 20.0 Σx = 15; Σy = 87.9; Σx2 = 55; Σy2 = 1,568.77; Σxy = 273.6 (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 three decimal places.) x = y = b = ŷ = + xarrow_forwardTemperature Gas Usage (thm) 37 1250 39 1375 41 980 44 875 47 750 48 730 49 765 53 510 56 480 58 300 A) Graph data and find axis, line of best fit (get exact values, round to three decimal places as needed). B) Pick one independent point and calculate expected value. Compare results of observed value. C) Calculate r-value and explain in context.arrow_forwardBighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 12.2 17.5 14.4 19.6 20.0 (c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.) r = ? r2 = ? What percentage of variation in y is explained by the least-squares model? __________ %(Round your answer to one decimal place.) incorrect answers: I submitted this question and was told this is the answer but it is NOT CORRECT. please help !! r=0.800 r2= 0.640 64% ( above answers are incorrect)arrow_forward
- Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 13.8 19.3 14.4 19.6 20.0 Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1554.45; Σxy = 274b) Find the equation of the least-squares line. (Round your answers to two decimal places.) ŷ = + x (c) Find r. Find the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = d) Test the claim that the population correlation coefficient is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t =arrow_forwardBighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 15.8 17.3 14.4 19.6 20.0 Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1,540.45; Σxy = 272 (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 three decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. (c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is…arrow_forwardBighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 12.2 20.9 14.4 19.6 20.0 Σx = 15; Σy = 87.1 ; Σx2 = 55; Σy2 =1577.17; Σxy = 275.6 (a) Draw a scatter diagram. (b) Find the equation of the least-squares line. (Round your answers to two decimal places.) ŷ = + x (c) Find r. Find the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = Explain what these measures mean in the context of the problem. The correlation coefficient r measures the strength of the linear relationship between a bighorn sheep's age and the mortality rate. The coefficient of determination r2 measures the explained…arrow_forward
- Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 12.2 20.9 14.4 19.6 20.0 Σx = 15; Σy = 87.1 ; Σx2 = 55; Σy2 =1577.17; Σxy = 275.6 d) Test the claim that the population correlation coefficient is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t = e) Find or estimate the P-value of the test statistic. P-value > 0.250 0.125 < P-value < 0.250 0.100 < P-value < 0.125 0.075 < P-value < 0.100 0.050 < P-value < 0.075 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 0.0005 < P-value < 0.005 P-value < 0.0005 Conclusion Reject the…arrow_forwardFinding a Prediction Interval. In Exercises 13–16, use the paired data consisting of registered Florida boats (tens of thousands) and manatee fatalities from boat encounters listed in Data Set 10 “Manatee Deaths” in Appendix B. Let x represent number of registered boats and let y represent the corresponding number of manatee deaths. Use the given number of registered boats and the given confidence level to construct a prediction interval estimate of manatee deaths. Boats Use x = 98 (for 980,000 registered boats) with a 95% confidence level.arrow_forwardExercise 1. Illustrate the value of the following t-distributions. a. two-tailed with a = 10% and df=10. b. one-tailed with a = 5% and df=18. c. two-tailed with a = 5% and n=29.arrow_forward
- The data given below is the expected points for a football team with first down and 10 yards to go from various points on the field. In the given table x stands for the number of yards from the goal and y stands for the expected points. r = X y 5.454 5.184 25 4.702 35 3.716 45 2.612 55 2.878 65 1.778 75 0.994 85 0.792 95 -0.642 555 a) Use Desmos (watch Video if you need help) to find the equation of the least squares (regression) line. to find the coefficient of correlation. (Round to 4 decimal places as needed.) Y 15 Does there appear to be a linear correlation? O No, there is no linear correlation between the data points because r is not equal to 0. Yes, the data points show linear correlation because r is close to -1. Yes, the data points show linear correlation because r is close to 1. O No, there is no linear correlation between the data points because r is negative. b) The equation of the least squares line is (Round to 2 decimal places as needed.)arrow_forwardBighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: 1. 3 4 12.2 17.5 14.4 19.6 20.0 A USE SALT Ex = 15; Ey = 83.7; Ex² = 55; Ey? = 1,446.61; Exy = 268.8 (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 three decimal places.) y = (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. y y 22 22 20 20 18 18 16 16 14 14 12 12arrow_forwardExample 10.9) Assume that the standard deviation o is 300 and n is 25. Calculate the standard error of the sample mean.arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill