0.2 Practice tests (1-4) and final exams  (Page 25/36)

2 . To complete a painting job requires four hours setup time plus one hour per 1,000 square feet. How would you express this information in a linear equation?

3 . A statistics instructor is paid a per-class fee of $2,000 plus $100 for each student in the class. How would you express this information in a linear equation?

4 . A tutoring school requires students to pay a one-time enrollment fee of $500 plus tuition of $3,000 per year. Express this information in an equation.

12.2: slope and Y -intercept of a linear equation

Use the following information to answer the next four exercises. For the labor costs of doing repairs, an auto mechanic charges a flat fee of $75 per car, plus an hourly rate of $55.

5 . What are the independent and dependent variables for this situation?

6 . Write the equation and identify the slope and intercept.

7 . What is the labor charge for a job that takes 3.5 hours to complete?

8 . One job takes 2.4 hours to complete, while another takes 6.3 hours. What is the difference in labor costs for these two jobs?

12.3: scatter plots

9 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.

10 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.

11 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.

12 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.

12.4: the regression equation

Use the following information to answer the next four exercises. Height (in inches) and weight (In pounds) in a sample of college freshman men have a linear relationship with the following summary statistics:
$\overline{x}$ = 68.4
$\overline{y}$ =141.6
s _x = 4.0
s _y = 9.6
r = 0.73
Let Y = weight and X = height, and write the regression equation in the form:
$\widehat{y}=a+bx$

13 . What is the value of the slope?

14 . What is the value of the y intercept?

15 . Write the regression equation predicting weight from height in this data set, and calculate the predicted weight for someone 68 inches tall.

12.5: correlation coefficient and coefficient of determination

16 . The correlation between body weight and fuel efficiency (measured as miles per gallon) for a sample of 2,012 model cars is –0.56. Calculate the coefficient of determination for this data and explain what it means.

17 . The correlation between high school GPA and freshman college GPA for a sample of 200 university students is 0.32. How much variation in freshman college GPA is not explained by high school GPA?

18 . Rounded to two decimal places what correlation between two variables is necessary to have a coefficient of determination of at least 0.50?

12.6: testing the significance of the correlation coefficient

19 . Write the null and alternative hypotheses for a study to determine if two variables are significantly correlated.

20 . In a sample of 30 cases, two variables have a correlation of 0.33. Do a t -test to see if this result is significant at the α = 0.05 level. Use the formula:
$t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$