STA2023 Extra Credit #1 1. Here are the summary statistics for the weekly payroll of a small company: Lowest salary = 250, mean salary = 500, median salary = 500, range = 1050, IQR = 300, Q1 = 350, standard deviation = 200. a. In the absence of outliers, do you think the distribution of salaries is symmetric, skewed to the left, or skewed to the right? b. Suppose the company gives everyone a $50 raise. Tell the new values of each of the summary statistics. New median salary = New IQR = c. Instead of a $50 raise, suppose the company gives everyone a 5% raise. Tell the new values of each of the summary statistics below. New median salary = New IQR = 2. The following is a list of test scores for the first test of a small stats class. Hint: use your calculator 76 98 78 66 60 50 81 57 a. Find the median. b. Find the IQR c. Find the mean d. Find the standard deviation 92 101 79 88 3. The histogram below shows the distribution of the number of hotdogs eaten for contestants at a hot dog eating contest. The 5-number summary is to the right. Histogram of number of hot dogs 16 Max Q3 Med Q1 Min 14 Frequency 12 10 8 6 51 26 23 18 11 4 2 0 5 10 15 20 25 30 35 number of hot dogs 40 45 50 55 a. Which summary statistic should you choose to summarize the center in these data? b. Which summary statistic should you choose to summarize the spread in these data? c. How many contestants should you classify as outliers? d. Write a brief description of this distribution (shape, center, spread). 4. Suppose the lengths of green beans for a particular farm are Normally distributed with a mean of 10 inches and a standard deviation of 1.5 inches. a. What is the z-score for a green bean that measures 12.3 inches? b. What percent of green beans measure between 6.79 inches and 11.8 inches? c. What percent of green beans measure more than 7.3 inches? d. What length represents the 75th percentile? e. The z-score for a particular green bean from this farm is z = 1.34. What does this tell us about the length of this green been? 5. Listed below are the Fat content (in grams) and Calories for several burgers at Biggies' Burgers Fast Food Restaurant. Fat (g) 20 Calories 410 23 490 31 570 33 590 37 580 38 630 40 670 43 680 a. Make a scatterplot of these data in your calculator using Fat as the explanatory (X) variable and Calories as the response (Y) variable. Describe each of the following in one word: Direction: _______________ Form: _______________ Strength: _______________ b. Find the correlation between Fat and Calories. c. Find the equation of the regression line to predict Calories from Fat. d. Use your equation to predict the number of calories for a burger with 25 grams of fat. 6. The ages (in years) and salaries (in thousands of dollars) of a random sample of engineers at a company were recorded. The data will be used to predict an engineer's salary from his/her age. A scatterplot of the data appeared linear in form and the least squares regression line calculated from the data is y 1.328x 21.5 . a. In terms of age and salary interpret the value of the slope of this line. (be sure to use units in your answer) b. Predict the salary for an engineer that is 30 years old. 7. The scatterplot below shows the total number of absences and final grades for the students in an Intro Stats course. A Regression to predict grade (in percentage points) from total number of absences (in days) has r = - 0.7878. Scatterplot of grade (%) vs abs (days) 100 grade (%) 90 80 70 60 0 2 4 6 8 abs (days) 10 12 14 16 a. Interpret the value of R2 in this context. b. The total number of absences averaged 3.15 days, with a standard deviation of 3.02 and the grades averaged 84.48% with a standard deviation of 9.93. Write the equation of the regression line. (Use 4 decimal places for r and 2 decimal places for all other values in your calculation - otherwise your answer may differ from mine). c. Interpret the slope of this line. d. Interpret the vertical intercept of this line. e. In terms of total number of absences and final grades, what can we say about a student that has a positive residual