Here is a bivariate data set. X y 59 42 80 116 59 73 52 56 84 97 52 10 61 48 60 72 62 39 Find the correlation coefficient and report it accurate to four decimal places. r = Hint: HelpThe following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. Year Retail Sales 0 35.851 3 108.426 6 141.781 9 169.256 12 202.297 15 222.266 Let S(t) be the retails sales in billions of dollars in t years since 1995. A linear model for the data is F(t) = 9.44t + 84.182. 220 210- 200- 190- 180 170 160 150- 140 130- 120- 110 100 90 6 12 804 Use the above scatter plot to decide whether the linear model fits the data well. O The function is a good model for the data. O The function is not a good model for the data Estimate the retails sales in the U. S. in 2014. billions of dollars. Use the model to predict the year that corresponds to retails sales of $239 billion.Statistics students in Oxnard College sampled 10 textbooks in the Condor bookstore and recorded the number of pages in each textbook and its cost. The bivan' ate data are shown below: Number of Pages (2:) Cost(y] 274 58. 14 569 90. 5'9 611 59.42 420 64.1 71 1 102. 21 698 98.75 3 51 64. n 973 1 1 7. 03 700 96 546 52.06 A student calculates a linear model 1; = :l :1: +:]. (Please show your answers to two decimal places) Use the model to estimate the cost when number of pages is 979. Cost = E (Please show your answer to 2 dedmal places.) Hint: Help F37 The table below shows the number of state-registerec automatic weapons and the murder rate for several Northwestern states. z 31 11.4 8.4 6.7 3.5 2.9 2.2 2.4 0.7 13.5 10.9 9.5 6.7 6.2 6.1 6.3 4.6 I = thousands of automatic weapons 1; = murders per 100,000 residents Determine the regression equation in y = ax + b form and write it below. (Round to2 decimal places} :1 A) How many murders per 100,000 residents can be expected in a state with 10.4 thousand automatic weapons? Answer = |:] Round to 3 decimal places. B} How many murders per 100,000 residents can be expected in a state with 3.6 thousand automatic weapons? Answer =:] Round to 3 dedmal places. Hint: Help Lid A regression was run to determine if there is a relationship between hours of study per week () and the final exam scores (y). The results of the regression were: y=ax+b a=5.572 b=26.72 -2=0.410881 r=0. 641 Use this to predict the final exam score of a student who studies 6 hours per week, and please round your answer to a whole number. Hint: HelpWhat is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below. Time 4 11 4 5 1 14 4 13 Score 71 72 64 72 50 86 59 82 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? ~ 0 H1: ? v * 0 The p-value is: (Round to four decimal places) c. Use a level of significance of or = 0.05 to state the condusion of the hypothesis test in the context of the study. O There is statistically significant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying. O There is statistically insignificant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the use of the regression line is not appropriate. O There is statistically significant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the regression line is useful. O There is statistically insignificant evidence to condude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying. d. 72 (Round to two decimal places) e. Interpret r2 : O There is a large variation in the final exam scores that students receive, but if you only look at students who spend a fixed amount of time studying per week, this variation on average is reduced by 78%. O There is a 78% chance that the regression line will be a good predictor for the final exam score based on the time spent studying. O Given any group that spends a fixed amount of time studying per week, 78% of all of those students will receive the predicted score on the final exam. 78% of all students will receive the average score on the final exam. f. The equation of the linear regression line is: y = I (Please show your answers to two decimal places) g. Use the model to predict the final exam score for a student who spends 6 hours per week studying. Final exam score = (Please round your answer to the nearest whole number.)What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 11 randomly selected games are shown below. Attendance 39 32 21 25 49 17 19 49 32 16 17 Runs 8 4 3 9 2 5 11 10 3 a. Find the correlation coefficient: T = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? v = 0 H1 : ? ~ * 0 The p-value is: (Round to four decimal places) c. Use a level of significance of or = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful. O There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance. O There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance. d. 72 = (Round to two decimal places) (Round to two decimal places) e. Interpret 72 : O 51% of all games will have the average number of runs scored. O There is a 51% chance that the regression line will be a good predictor for the runs scored based on the attendance of the game. O Given any fixed attendance, 51% of all of those games will have the predicted number of runs scored. O There is a large variation in the runs scored in baseball games, but if you only look at games with a fixed attendance, this variation on average is reduced by 51%. f. The equation of the linear regression line is: y = (Please show your answers to two decimal places) g. Use the model to predict the runs scored at a game that has an attendance of 32,000 people. Runs scored = (Please round your answer to the nearest whole number.)Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits in millions of dollars). Determine if there is a significant positive linear correlation between advertising cost and profit . Use a significance level of 0.05 and round all values to 4 decimal places. Advertising Cost Profit 3 19 4 15 5 20 6 20 7 21 8 32 9 20 10 29 11 27 Ho: p = 0 Ha: p > 0 Find the Linear Correlation Coefficient Find the p-value p-value = The p-value is O Less than (or equal to) or O Greater than or The p-value leads to a decision to O Reject Ho O Accept Ho O Do Not Reject Ho The conclusion is O There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit. O There is a significant negative linear correlation between advertising expense and profit. O There is a significant linear correlation between advertising expense and profit. O There is a significant positive linear correlation between advertising expense and profit.A study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below. Movies 0 3 2 2 9 4 5 4 10 Books 15 5 12 7 0 6 1 8 0 a. Find the correlation coefficient: T = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? ~ = 0 H1 : ? v * 0 The p-value is: Round to 4 decimal places. c. Use a level of significance of or = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically insignificant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the use of the regression line is not appropriate. O There is statistically significant evidence to condude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the regression line is useful. O There is statistically significant evidence to condude that a person who watches fewer movies will read fewer books than a person who watches fewer movies. O There is statistically significant evidence to conclude that a person who watches more movies will read fewer books than a person who watches fewer movies d. 72 = (Round to two decimal places) e. Interpret r : O 76% of all people watch about the same number of movies as they read books each year. O There is a 76% chance that the regression line will be a good predictor for the number of books people read based on the number of movies they watch each year. O There is a large variation in the number books people read each year, but if you only look at people who watch a fixed number of movies each year, this variation on average is reduced by 76%. O Given any fixed number of movies watched per year, 76% of the population reads the predicted number of books per year. f. The equation of the linear regression line is: y = I (Please show your answers to two decimal places) g. Use the model to predict the number of books read per year for someone who watches 5 movies per year. Books per year = (Please round your answer to the nearest whole number.)