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10. [0.44/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.3.013.MI.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (a) Suppose n = 6 and the sample correlation coefficient is r = 0.888. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) LO USE SALT t = critical t = Conclusion: O Yes, the correlation coefficient p is significantly different from 0 at the 0.01 level of significance. No, the correlation coefficient o is not significantly different from 0 at the 0.01 level of significance. (b) Suppose n = 10 and the sample correlation coefficient is r = 0.888. Is / significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) critical t12. [0.23/1 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 result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar. 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 vaccination for 8 weeks. Results are shown in the following time series. Original Time Series Week 2 3 8 Buildup Factor 2.3 4.6 6.2 7.5 8.0 9.4 10.6 12.1 To construct a serial correlation, we simply use 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 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 LA USE SALT For convenience, we are given the following sums. Ex = 48.6, Ey = 58.4, Ex = 385.86, Ey? = 526.98, Exy = 448.7 (a) 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.) b = If the buildup factor was x = 5.2 one week, what would you predict the buildup factor to be the next week? (Round your answer to two decimal places.) (b) Compute the sample correlation coefficient / and the coefficient of determination . (Round your answers to four decimal places.) Test p > 0 at the 1% level of significance. (Round your answers to three decimal places.) critical t4. [-/1 Points] DETAILS BBUNDERSTAT12 9.R.004. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose that for x = 3, the predicted value is y = 4. The data pair (3, 5) is part of the sample data. What is the value of the residual for x = 3? Need Help? Read It5. [0.3/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.R.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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: 5 12.6 19.7 14.4 19.6 20.0 Ex = 15; Zy = 86.3; Ex? = 55; Zy? = 1538.37; Exy = 273.6 a) Draw a scatter diagram. Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties. Help WebAssign. Graphing Tool(b) Find the equation of the least-squares line. (Round your answers to two decimal places.) 7 = (c) Find r. Find the coefficient of determination . (Round your answers to three decimal places.) Explain what these measures mean in the context of the problem. O Both the correlation coefficient r and coefficient of determination / measure the strength of the linear relationship between a bighorn sheep's age and the mortality rate. 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 / measures the explained variation in mortality rate by the corresponding variation in age of a bighorn sheep. O The coefficient of determination r measures the strength of the linear relationship between a bighorn sheep's age and the mortality rate. The correlation coefficient of measures the explained variation in mortality rate by the corresponding variation in age of a bighorn sheep. O The correlation coefficient / measures the strength of the linear relationship between a bighorn sheep's age and the mortality rate. The coefficient of determination r measures the explained variation in mortality rate by the corresponding variation in age of a bighorn sheep. (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 = Find or estimate the P-value of the test statistic. O P-value > 0.250 0.125 D.250 D 0.125 D. D Reject the null hypothesi cient evidence that p > D. Fall to reject the null hypothes dence that p > 0. Fail to reject the null hypothesis. There is Insufficient evidence that p > 0. el If someone had x - 9 job changes, what does the le pares line predict for y, the a thousand dollars f) Find S,. (Round your answer to three decimal places.) (g) Find a 90%% confidence Interval for the annual salary of an Incivic scimal places.) ower limit thousand dollars upper limit sand dollars (h) Test the daim that the slope s of the population least nificance. (Round your test statistic to three decimal places.) Find or estimate the Avalue of the test statistic. P-value > 0.250 D 0.125 0. ant evidence that # > 0. e that # > D. Fail to reject the null hypothesis. There is Insufficient evidence that # > 0. 1) Find a 90% confidence interval for if and Interpret its meaning. (Round your answers to three decimal places.) ower limit