Name:______Date:______Score:_____/67
Advanced Placement Statistics
MANDATORY
Summer Assignment 2016
- This assignment reviews some of the basic skills/concepts I would like you to know/understand prior to taking this course; it also addresses some of the new content that we will begin to learn at our MANDATORY summer sessions in August!
- You will have the opportunity to complete this entire assignment at our summer academy in August—bring it with you!
- This assignment also demonstrates that you are prepared for the workload and responsibility that comes with an AP course!
- Due Date: on/before the first day of school
- Most of us will complete this during our summer AP sessions!
- To take AP Statistics it is required that you complete this assignment and attend our summer academy
- This will serve as your first test grade for the course.
- A graphing calculator is required to complete this assignment. Additionally, a graphing calculator is required for this course.
- Be sure to continually check the EHHS AP Stat blog over the summer—here you will find helpful hints, links with resources you can use for its completion, class updates/news, and even potential credit opportunities! Get in the habit of checking this blog every day—it’s our number 1 resource for questions/answers/course info!
- If at any point over the summer you have questions feel free to email me at . I’m more than willing to help so you can start off with an A! You can always feel free to email me at any time!
Class Blog: Check it!
Use the graph shown below to answer questions 1 – 8. The graph shows the predicted ice cream sales ($) based on the temperature (°Celsius) for a given day, for a local ice cream shop.
1. What is the (approximate) y-coordinate of the point with the largest x-coordinate? Provide units with your answer. (1 point)
2. What is the (approximate) x-coordinate of the point with the lowest y-coordinate? Provide units with your answer. (1 point)
3. Does the graph shown have a positive or negative association? Circle the appropriate word for each of the bolded options: (2 pts)
There is a positive/negative association between temperature and predicted ice cream sales. Generally, as temperature increases/decreases, predicted ice cream sales increase/decrease.
4. Write the coordinates of the circled point (from the graph above).(2 points)
5. Interpret the meaning of the coordinate pair for this circled point in a complete sentence (in context!)—what does this point tell us about temperature/ice cream sales? Be detailed! (2 points)
6. For the scatter plot above, what is the explanatory variable (also known as the independent variable)? (1 point)
7. For the scatter plot above, what is the response variable (also known as the dependent variable)? (1 point)
8. A statistician found the equation of the line of best fit (linear regression equation); the equation was , where x represents the temperature (in °Celsius) and represents the predicted ice cream sales (in $). Interpret the meaning of the slope of this line, in context. (2 points)
Use the data set below (and your responses to #9) to answer questions 9 – 12.
9. Use your graphing calculator to find the linear regression equation (line of best fit), correlation, and coefficient of determination for the data set below. Round to three decimal places. See below for calculator help/instructions. (4pts).
x (# of hours) / 2 / 5 / 6 / 8 / 9 / 10Y (Population of Bacteria, in thousands) / 4.19 / 8.46 / 9.35 / 15.06 / 21.98 / 29.72
Linear Regression Equation (Line of Best Fit): ______
Correlation (r) = ______Coefficient of Determination () = ______
Calculator Instruction: To find the linear regression equation, correlation, and coefficient of determination…
- First enter the data in your calculator: press STAT, go to EDIT, and then you can see all the lists to enter data in your calculator. If you need to clear a list, highlight the title of the list (L1, L2, etc.) , press clear and then enter. Enter all of your x-values in L1, and enter all of your y-values in L2. Always double check for typos.
- Now, press 2nd then MODE to quit to a home screen. From here, press STAT, scroll right to CALC, then choose number 8, LinReg(a+bx). You will either have to enter your xlist (L1) and ylist (L2), or you will have to type L1, L2 after the LinReg, depending on the model of your calculator. Then, press enter (or calculate, depending on your calculator model).
- Need more help? Do some Googling! Look up how to enter data in a TI-8__, then how to do a linear regression!
- **If your calculator does not show r and R^2, you need to turn these capabilities on. To do so, press 2nd 0 to go to the Catalog. Then, scroll down to “DiagnosticOn.” Press enter. Then, press enter again and the calculator will say “Done.” Now, if you re-do the LinReg(a + bx), R and R^2 will appear below the equation.
10. Use the equation calculated above to predict the population of bacteria after 15 hours. Show all of your work in the space below. (2 points)
11. Suppose the actual population of bacteria after 15 hours was 45 thousand. How far off was your prediction? In statistical terms, calculate the residual. (Residual = actual value – predicted value) (2 points)
12. Consider the correlation, r, calculated above. Use this value to describe the strength and direction of the correlation between the number of hours passed and the population of bacteria. Write your answer in a complete sentence, in context. (3 points)
Use the context and data provided below to create the graphical displays and find the summary statistics in questions 13 –17.
It appears that El Nino, the periodic warming of the Pacific Ocean west of South America, affects the monsoon rains that are essential for agriculture in India. Here are the monsoon rainfall amounts (in millimeters) for 23 strong El Nino years between 1871 and 2004:
628 / 669 / 740 / 651 / 710 / 736 / 717 / 698 / 653 / 604781 / 784 / 790 / 811 / 830 / 858 / 858 / 896 / 806 / 790
792 / 957 / 872
13. Use the axes below to create a histogram to show the distribution of monsoon rainfall amounts. Use a minimum x-value of 600, a maximum x value of 1000, and an x-scale of 50 (count by 50’s on the x-axis) . Be sure to include all appropriate labels and a title. (5 points)
The steps below explain how we can use our graphing calculator to quickly find summary statistics for a given data set. Use your graphing calculator to find each value below (questions 14-16).
a)Enter the data in L1. To do so, press STATEDIT
- To clear L1, highlight the title L1 with your cursor and press CLEARENTER
b)Go to the home screen. (Press 2ndMODE to “Quit”)
c)Generate the 1 Variable Statistics. To do so, press STATScroll right to CALChighlight 1-Var Stats and press ENTER
d)Define where your data is stored. Type L1 after 1-Var Stats. To type L1, press 2nd1.
e)The mean and standard deviation can now be seen. Scroll down to see the 5 number summary.
14. Find the mean rainfall amount. The mean is denoted by “x-bar” on the calculator. (1 point)
15. Find the 5 number summary for rainfall amounts: the minimum, first quartile (Q1), median, third quartile (Q3), and the maximum. Label your answers. (5 points)
16. Find the range of rainfall amounts. (1 point)
17. Use the axis below to create a boxplot to show the distribution of monsoon rainfall amounts in India. Be sure to include all appropriate labels and a title. (5 points)
18. The table below shows the score distribution for AP Statistics Exam Scores in May, 2015. Create a bar graph to display this score distribution. Be sure to include all necessary labels and a title. (4 points)
AP Exam Score / # of Students1 / 10
2 / 9
3 / 15
4 / 24
5 / 7
Use the information below (from a 2010 AP exam) to answer questions 19 -- 22.
19. What is the probability that a randomly selected adult from this poll is a not a high school graduate or obtains news primarily from cable television? Be sure to show your work (a fraction) and your answer (a decimal) in the space below. (2 points)
20. What is the probability that a randomly selected adult primarily obtains news from the internet? Be sure to show your work (a fraction) and your answer (a decimal) in the space below. (2 points)
21. What is the probability that someone who is a college graduate primarily obtains news from the internet? Be sure to show your work (a fraction) and your answer (a decimal) in the space below. (2 points)
22. Compare your answers to questions 21 and 22. Based these answers, do you think “being a college graduate” and “obtaining news primarily from the internet” are independent? Explain your reasoning. (3 points)
Multiple Choice Section: Answer each AP multiple choice question below. (each @ 2 points)
23. A teacher has two different mathematics courses. Her first class has 29 students and had an average score of 79 on the first exam. Her second class has 20 students and had an average score of 84 for the first exam. What is the overall average for the first exam (for both classes, combined)?
a. 81.5b. 83.05c. 79.88d. 81.04e. 79.42
24. A wildlife biologist is interested in the relationship between the number of chirps per minute for crickets (y) and temperature. Based on the collected data, the least squares regression line is (where x is the number of degrees Fahrenheit by which the temperature exceeds 50°). Which of the following best describes the meaning of the slope of the least squares regression line (line of best fit)?
a. For each increase in temperature of 1°F, the estimated number of chirps per minute increases by 10.53.
b. For each increase in temperature of 1°F, the estimated number of chirps per minute increases by 3.41.
c. For each increase of one chirp per minute, there is an estimated increase in temperature of 10.53°F.
d. For each increase of one chirp per minute, there is an estimated increase in temperature of 3.41°F.
e. The slope has no meaning because the units of measure for x and y are not the same.
25. Jason wants to determine how age and gender are related to political party preference in his town. Voter registration lists are stratified by gender and age-group. Jason selects a simple random sample of 50 men from the 20 to 29 age-group and records their age, gender, and party registration (Democratic, Republican, neither). He also selects an independent simple random sample of 60 women from the 40 to 49 age-group and records the same information. Of the following, which is the most important observation about Jason’s plan?
a. The plan is well conceived and should serve the intended purpose.
b. His samples are too small.
c. He should have used equal sample sizes.
d. He should have randomly selected the two age groups instead of choosing them nonrandomly.
e. He will be unable to tell whether a difference in party affiliation is related to differences in age or to the difference in gender.
Use the information below to answer questions 26-27:
Left-handedness is the preference for the left hand over the right for everyday activities such as writing. Researchers would like to conduct a study to determine if left-handed teens differ significantly in their ability to memorize facts than right-handed teens.
26.The explanatory (independent) variable in this study is:
a. ability to memorize factsb. Agec. Handednessd. Researcherse. None of these
27. The response (dependent) variable in this study is:
a. ability to memorize factsb. Agec. Handednessd. Researcherse. None of these
28. The Physicians’ Health Study was a large medical experiment. It included 22,000 male physicians, and attempted to determine if aspirin can help in heart attack prevention. In the study, one group of (approximately) 11,000 physicians took one aspirin every other day; a control group took a placebo every other day. Several years later, it was determined that the physicians that took aspirin had significantly fewer heart attacks than those physicians in the control group (who took a placebo). Which of the following statements explains why it is NOT appropriate to say that everyone should take an aspirin every other day?
I. The study included only physicians, and different results may occur in individuals in other occupations.
II. The study included only males, and there may be different results for females.
III. Although taking aspirin may be helpful in preventing heart attacks, it may be harmful to some other aspects of health.
- I onlyb. II onlyc. III onlyd. II and III onlye. I, II, and III
29. Use the equation provided to predict the GPA for a student who works for 12 hours each week:
- 3.24b. 3.4c. 5.16d. 3e. 3.56
30. Suppose you have a bag of marbles; there are 13 red and 7 blue marbles. First, your friend draws a red marble and takes it home. Now, you draw a marble from the bag (after your friend)—what is the probability that yours is also red?
a. b. c. d. e.