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 78 60 81
|
92
|
79
|
|
98 66 50 57
|
101
|
88
|
a. Find the median.
b. Find the IQR
c. Find the mean
d. Find the standard deviation
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.
Max 51
Q3 26
Med 23
Q1 18
Min 11
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
|
23
|
31
|
33
|
37
|
38
|
40
|
43
|
|
Calories
|
410
|
490
|
570
|
590
|
580
|
630
|
670
|
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 yˆ = 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.
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.