Q #1

5. [0.5/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.008. MY NOTES ASK YOUR TEACHER Over the past decade, there has been a strong positive correlation between teacher salaries and prescription drug costs. (a) Do you think paying teachers more causes prescription drugs to cost more? Explain your answer. No. A strong correlation does not imply causation. O No. A strong correlation implies causation. Yes. A strong correlation does not imply causation. O Yes. A strong correlation implies causation. (b) What lurking variables might be causing the increase in one or both of the variables? Explain your answer. This answer has not been graded yet Need Help? Read It Watch it6. [0.5/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.010. MY NOTES ASK YOUR TEACHER Over the past 30 years in the United States, there has been a strong negative correlation between the number of infant deaths at birth and the number of people over age 65. (a) Is the fact that people are living longer causing a decrease in infant mortalityes at birth? Explain your answer. No. A strong correlation implies causation. No. A strong correlation does not imply causation. O Yes. A strong correlation implies causation. Yes. A strong correlation does not imply causation. [b) What lurking variables might be causing the increase in one or both of the variables? Explain your answer. This answer has not been graded yet. Need Help? Read It7. [0.75/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.014.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOT 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. 36 y 40 35 15 30 27 17 LA USE SALT (a) Make a scatter diagram of the data and visualize the line you think best fits the data. 40 40 40 35 35 as percentage) y (average cost as percentage) as percentage) as percentage) 30 y (average cost y (average cost y (average cost 25 25 20 20 20 10 20 30 40 50 60 70 10 20 30 40 50 60 70 10 20 30 40 50 60 70 10 20 30 40 50 60 70 x (average number x (average number x (average number x (average number O 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 strong and positive O strong and negative low and positive O moderate and positive O low and negative (c) Use a calculator to verify that Ex = 131, Ex2 = 6479, Ey = 149, Ey? = 4743, and Exy = 2977. Computer. (Round your answer to four decimal places.)8. [0.67/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 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 esents 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 3 23 15 30 25 LA USE SALT (a) Make a scatter diagram of the data. Then visualize the line you think best fits the data. 70 30 8 8 8 3 60 25 50 y (annual number of burglaries) y (annual number of burglaries) y (annual number of burglaries) y (annual number of burglaries) 20 40 30 15 30 20 20 10 10 15 20 25 30 10 15 20 25 30 20 30 40 50 60 70 20 30 40 50 60 70 x (student enrollment (in thousands)) O 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, Zy? = 9270 and Exy = 5418.2. Compute r. (Round your answer to four decimal places.)10. [0.5/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.020.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Examine the computation formula for r, the sample correlation coefficient. (a) 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 same because the formula is not dependent on the symbols. O The result is different because the formula is dependent on the symbols. O The result is different b ent 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 depend Int on which values are the x values and which values are the y values. The result is different be ch values are the x values and which values are the y values. O The result is the same because the formula is lues 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.) (ii ) x y 4 LO USE SALT () Need Help? Read It Watch it|S Shutterfly x |@ Home | MyOttawa x |Content x |Activity Stream * @ Home | Ottawa University * |Content x VA 9.1 Hmwk - Scatter Diagrams an X + X C @ https://www.webassign.net/web/Student/Assignment-Responses/last?dep=28262126#question4738612_10 Need Help? Read It Watch it 11. [0.32/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.021.5. 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 o 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 Irl 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 Coefficient - 0.05 - 0.01 - 0.05 a - 0.01 7 - 0.05 4 - 0.01 1.00 1.00 13 0.53 0.68 23 0.41 0.53 0.95 0.99 14 0.53 0.66 24 0.40 0.52 0.88 096 IS 0.51 0.64 25 0.40 051 0.81 092 16 0.50 0.61 26 0.39 a.50 0.75 0.87 0.48 0.61 27 0.38 0.49 0.71 083 18 0.47 0.59 28 0.37 0.48 0.67 080 19 0.46 0.58 29 0.37 0.63 0.76 20 044 0.56 30 0.36 0.46 11 0.60 0.73 043 ass (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 12 LO USE SALT critical Conclusion O 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 e to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is insu ce to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is suffir and 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 y 40 975 992 100 65 935 970 940 critical r Conclusion O Reject the null hypothesis, there is suffic cyclones are correlated. O Reject the null hypothesis, there is insufficient evid wind speed for cyclones are correlated. O Fail to reject the null hypothesis, there is insufficient evid ence to show peed for cyclones are correlated. O Fail to reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Need Help? Read It Watch it Submit Answer Type here to search 7:07 AM 41.F Cloudy ~ 6 0 7 () 4/1/2022 2412. [-/1 Points] DETAILS 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 a = 0.05 * = 0.01 a = 0.05 a = 0.01 a = 0.05 = 0.01 1.00 1.00 13 0.53 0.68 25 0.41 0.53 0.95 0.99 0.66 0.40 0.52 0.88 096 15 0.51 0.64 25 0.40 0.51 0.81 0.92 16 0.50 0.61 26 0.39 7 0.75 0.87 17 0.48 0.61 27 0.38 0.49 8 0.71 0.83 18 0.47 0.59 28 0.37 0.48 9 0.67 0.80 19 0.46 0.58 29 0.37 0.47 10 0.63 0.76 20 Q44 0.56 036 046 11 0.60 0.73 21 043 0.55 12 058 0.71 22 0.42 (a) Is a sample correlation coefficient p = 0.81 significant at the a = 0.01 level based on a sample size of n = 4 data pairs? What about n = 14 data pairs? (Select all that apply.) O No, because the absolute value of the given correlation fficient is smaller than that for a sample size of n = 14 and a = 0.01. O Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 14 and a = 0.01. O No, because the absolute value of the given cor tion coefficient is greater than or equal to that for a sample size of n = 4 and a = 0.01. O No, because the absolute value of the given correlat coefficient is greater than or equal to that for a sample size of n = 14 and a = 0.01. O No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 4 and a = 0.01. O Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 4 and a = 0.01. O Yes, because the absolute value of the given = 14 and a = 0.01. Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 4 and a = 0.01. (b) Is a sample correlation coefficient p = 0.40 significant at the a = 0.05 level based on a sample size of n = 16 data pairs? What about n = 30 data pairs? (Select all that apply.) O No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 30 and a = 0.05. O No, because the absolute value of the given = 30 and a = 0.05 O Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 30 and a = 0.05. O Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 16 and a = 0.05. O No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 16 and a = 0.05. O No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 16 and a = 0.05. O Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 30 and a = 0.05. O Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 16 and a = 0.05. (c) Is it true that in order to be significant, a p value must be larger than 0.90? larger than 0.70? larger than 0.50? What does sample size have to do with the significance of p? Explain your answer. O Yes, a larger correlation coefficient of 0.70 means that the data will be significant. O Yes, a larger correlation coe s that the data will be significant. O No, sample size has no bearing on whether or not the correlation coefficient might be significant. O No, a larger sample size means that a smaller absolute value of the correlation coefficient might be significant. O Yes, a larger correlation coefficient of 0.90 means that the data will be significant. Need Help? Read ItVerify that Ex - 149, Ex2 - 3463, Ty - 244, 1y2- 9584, and Exy - 5734. ampute r. (Round your The data in part (a) represent average annual hours lost per person and average annual gallons of fuel wasted per person er person in traffic delays. Suppose that Instead of using average data for different cities, you seles from each city and reasured the annual number of hours lost x for that person and the annual gallons of fuel wasted y for the same person. * [hr) 24 4 y (gal) 64 8 1 (b) Compute x and y for both sets of data pairs and compare the averages. (Round your four decimal places.) Data Data Compute the sample standard deviations s, and s, for both sets of data pairs and compare the standard deviations. (Round your anawers to four decimal places.) Data 1 In which set are the standard deviations for x and y larger? O The standard deviations for x and y are larger for the first set of data. # The standard deviations for x and y are large e second set of data. The standard deviations for x and y are the same for both sets of data. Look at the defining formula for r. Why do smaller standard deviations s, and s, tend to increase the value of ?? Dividing by smaller numbers results in a smaller value. # Dividing Its In a larger value. Multiplying by small (c) Make a scatter diagram for the second set of data pairs. 40 yogali yogall Fugal 10 20 30 40 50 20 10 15 20 30 35 20 30 40 50 10 15 20 25 O x(hr) * (hr) x (hr) x (hr) verify that Ex - 169, Ex- - 4887, Ty - 266, Ly' - 13,602, and Exy - 7657. Computer. (Round your answer to four decimal places.) d) Compare r from part (a) with / from part (b). Do the data ents? No, the data for averages do not have a higher reasurements. Yes, the data for aver le in a dty.14. [0.32/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.024. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Previously, you studied linear combinations of independent random variables. What happens if the variables are not independent? A lot of mathematics can be used to prove the following: Let x and y be random variables with means u, and u , variances of,and 2 , and population correlation coefficient p (the Greek letter rho). Let a and b be any constants and let w = ax + by for the following formula. = aux + buy 2 In this formula, r is the population correlation coefficient, theoretically computed using the population of all (x, y) data pairs. The expression ,6 0 is called the covariance of x and y. If x and y are independent, then p = 0 and the formula for ", reduces to the appropriate formula for independent variables. In most real-world applications the population parameters are not known, so we use sample estimates with the understanding that our conclusions are also estimates. Do you have to be rich to invest in bonds and real estate? No, mutual fund shares are available to you even if you aren't rich. Let x represent annual percentage return (after expenses) on the Vanguard Total Bond Index Fund, and let y represent annual percentage return on the Fidelity Real Estate Investment Fund. Over a long period of time, we have the following population estimates. 4 2 7.35, 0 ~ 6.55, 1 = 13.17, = 18.56, P = 0.422 (a) Do you think the variables x and y are independent? Explain your answer. O No. Interest rates probably has no effect on the investment returns. Yes. Interest rate probably affects both investment returns. No. Interest rate probably affects both investment returns. Yes. Interest rates probably has no effect on the investment returns. (b) Suppose you decide to put 65% of your investment in bonds and 35% in real estate. This means you will use a weighted average w = 0.65x + 0.35y. Estimate your expected percentage return #, and risk ow " w (c) Repeat part (b) if w = 0.35x + 0.65y. L W d) Compare your results in parts (b) and (c). Which investment has the higher expected return? Which has the greater risk as measured by w? Ow = 0.35x + 0.65y produces higher return with lower risk as measured by w. O w = 0.35x + 0.65y produces higher return with greater risk as measured by ow. Ow = 0.65x + 0.35y produces higher return with lower risk as measured by ow. Both investments produce return with the same risk as measured by w. O w = 0.65x + 0.35y produces higher return with greater risk as measured by ow. Need Help? Read It