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7. [0.75/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.014.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims. 30 27 70 40 LO USE SALT (a) Make a scatter diagram of the data and visualize the line you think best fits the data. 40 40 40 as percentage) y (average cost as percentage) as percentage) as percentage) y (average cost y (average cost y (average cost - 25 20 20 10 20 30 40 50 60 70 10 20 30 40 50 60 70 20 30 50 60 70 10 20 40 50 60 70 xaverage number x (average number x (average number x(average number of employees) of employees) of employees) of employees) (b) Would you say the correlation is low, moderate, or strong? positive or negative? O moderate and negative O strong and positive strong and negative O low and positive moderate and positive O low and negative (c) Use a calculator to verify that Ex = 131, Ex? = 6479, Ey = 149, Ey? = 4743, and Exy = 2977. Computer. (Round your answer to four decimal places.) = -0.9858. [0.67/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT 12 9.1.018.MI.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Let x be a variable that represents student enrollment (in thousands) on a university campus, and let y be a variable that represents the number of burglaries in a year on the university campus. A random sample of n = 8 universities in California gave the following information about enrollments and annual burglary incidents. 13.9 31.0 24.5 14.3 7.5 27.7 16.2 20.1 22 69 39 23 15 30 15 25 LO USE SALT (a) Make a scatter diagram of the data. Then visualize the line you think best fits the data. 70 30 60 25 25 8 8 8 8 3 50 y (annual number of burglaries) y (annual number of burglaries) y (annual number of burglaries) y (annual number of burglaries) 20 20 40 30 15 20 20 10 10 10 15 20 25 30 10 15 20 25 30 20 30 40 50 60 20 30 40 50 60 70 x (student enrollment (in thousands)) x (student enrollment (in thousands)) x (student enrollment (in thousands)) x (student enrollment (in thousands)) (b) Use a calculator to verify that Ex = 155.2, Ex? = 3448.94, Zy = 238, Ey? = 9270 and Exy = 5418.2. Computer. (Round your answer to four decimal places.) 0.818 X10. [0.5/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.020.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Examine the computation formula for r, the sample correlation coefficient. (@) In the formula for r, if we exchange the symbols x and y, do we get a different result or do we get the same (equivalent) result? Explain your answer. The result is the sam pendent on the symbols. The rest the symbols. O The result is different b it on the symbols. O The result is the same because the formula is dependent on the symbols. (b) If we have a set of x and y data values and we exchange corresponding x and y values to get a new data set, should the sample correlation coefficient be the same for both sets of data? Explain your answer. O The result is different because the formula is dependent on which values are the x values and which values are the y values. O The result is different beca the formula is not dependent on which values are the x values and which values are the y values. O The result is the same because the formula is dependent on which values are the x values and which values are the y values. The result is the same because the formula is not dependent on which values are the x values and which values are the y values. (c) Compute the sample correlation coefficient / for each of the following data sets and show that r is the same for both. (Round your answers to four decimal places.) LO USE SALT (i) 0.466 (1i) 0.46 Need Help? Read It Watch it11. [0.32/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.021.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient p (Greek letter rho)? You do not know how to build the formal structure of hypothesis tests of p yet. However, there is a quick way to determine if the sample evidence based on p is strong enough to conclude that there is some population correlation between the variables. In other words we can use the value of r to determine if p # 0. We do this by comparing the value |) to an entry in the correlation table. The value of a in the table gives us the probability of concluding that p # 0 when, in fact, p = 0 and there is no population correlation. We have two choices for a: a = 0.05 or a = 0.01. Critical Values for Correlation Confident = 0.05 . = 0.01 = 0.05 4 = 0.01 " a = 0.05 =0.01 1.00 1.00 0.53 0.68 0.41 053 14 ass 24 0.40 052 0.51 051 0.81 0.92 25 0.50 0.61 Q.39 0.50 0.75 0.87 17 048 a.61 27 0.38 0.71 0.67 047 10 0.63 Q.76 044 ase ass 30 03s 0.46 0.60 0.73 043 0.58 071 Q42 (a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of Irl large enough to conclude that weight and age of Shetland ponies are correlated? Use a = 0.05. (Round your answer for r to four decimal places.) x 3 y 60 95 140 174 18 8 LO USE SALT critical Conclusion Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. O Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. (b) Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of Irl large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use a = 0.01. (Round your answer for r to four decimal places.) * 1004 5 992 y 40 100 65 5 970 145 7412. [0.34/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER In this problem, we use your critical values table to explore the significance of r based on different sample sizes. Critical Values for Correlation Coefficient "