AP Statistics

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1 AP Statistics Welcome to AP Statistics. I am looking forward to having you in class next year. Advanced Placement courses are designed to expose you to college level curriculum and higher expectations. In order to be ready to hit the ground running in September, you have some preliminary work to complete on your own. This work is due August 15 th by 3 pm. You may return it to the school or submit it on Schoology. The Schoology code for our AP Statistics group is MN65K-DRVMG. Your work is also posted there in case you misplace this packet. The vocabulary and a lot of the problems require you to answer on another sheet of paper. Please make sure you show all your work and staple it all together. Make sure your work is neat and organized. If you choose to submit through Schoology, I must be able to clearly see your answer to every problem and vocabulary. I highly recommend you purchase a TI-84 calculator before school begins. Some questions in this packet may be easier to answer if you have a TI 84 calculator and the book will show you what steps to follow. If you cannot purchase your own, you will be able to loan one once we return to school in the Fall. If you absolutely need to reach me over the summer, you can send me a Schoology message or me at Jessica.roach@cape.k12.de.us

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3 The following is work on the first three chapters from your textbook Practice in Statistics. In every section please define the vocabulary words and provide an example. Your example may be a picture in some situations. For your benefit you may want to write your definitions in your own words, not copy directly from the green box (this may require you to read the paragraph before the green box.) Remember you will be tested on this shortly after we return to school and it will help if you understand what you wrote back in July. Chapter 1 Introduction 1. Individual 2. Variable 3. Categorical variable 4. Quantitative variable 5. Distribution Answer the following questions and then state if your answer is a categorical or quantitative variable. If quantitative, in what units was the variable measured? Question Variable Units What is your gender? How old are you? When is your birthday? What is your height? What hand do you write with? What grade did you receive last year in your math course? What is your favorite genre of music? Section Marginal distribution 2. Conditional distribution 3. Association 4. Simpson s paradox

4 Section Mode 2. Range 3. Symmetric 4. Skewed right 5. Skewed left 6. Unimodal 7. Bimodal 8. Multimodal 9. Outlier Below is a table of the number of golds won by each country at the 2018 Winter Olympics.

5 a) Make a dotplot to display the data. b) Describe the overall pattern of the distribution and any deviations from that pattern. c) Sketch a dotpolot for a distribution that is skewed to the left. d) Suppose that you and your friends emptied your pockets of coins and recorded the year marked on each coin. The distribution of dates would be skewed to the left. Explain why. b) Describe the shape, center, and spread of the distribution.

6 b) Describe the distribution.

7 Section Mean 2. Median 3. Interquartile Range 4. The five-number summary 5. Standard Deviation 6. Variance Feeling Sleepy? The first four students to arrive for a first-period statistics class were asked how much sleep (to the nearest hour) they got last night. Their responses were 7, 7, 9, and 9. a) Find the standard deviation. b) Interpret the value sx you obtained in (a). c) Do you think it s safe to conclude that the mean amount of sleep for all 30 students in this class is close to 8 hours? Why or Why not? SD contest This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed. a) Choose four numbers that have the smallest possible standard deviation. b) Choose four numbers that have the largest possible standard deviation. c) Is more than one choice possible in either (a) or (b)? Explain. Section Percentile 2. Standardized value (z-score) 3. Density curve

8 Run Fast Peter is a star runner on the track team. In the league championship meet, Peter records a time that would fall at the 80 th percentile of all his race times that season. But his performance places him at the 50 th percentile in the league championship meet. Explain how this is possible. SAT versus ACT Eleanor scores 680 on the SAT Mathematics test. The distribution of SAT scores is symmetric and single-peaked, with mean 500 and standard deviation 100. Gerald takes the Act Mathematics test and scores 27. ACT scores also follow a symmetric, single-peaked distribution but with mean 18 and standard deviation 6. Find the standardized scores for both students. Assuming that both tests measure the same kind of ability, who has the higher score? Teacher raises A school system employs teachers at salaries between $28,000 and $60,000. The teachers union ad the school board are negotiating the form of next year s increase in the salary schedule. a) If every teacher is given a flat $1000 raise, what will this do to the mean salary? To the median salary? Explain your answers. b) What would a flat $1000 raise do to the extremes and quartiles of the salary distribution? To the extremes and quartiles of the salary distribution? To the standard deviation of the teacher s salaries? Explain your answer. Density Curve Sketch a density curve that might describe a distribution that has a single peak and is skewed to the left. Section Normal distribution and Normal curve 2. The rule 3. Standard Normal distribution 4. The standard Normal table 5. Normal probability plot Hot Cheetos The distribution weight of 5-ounce bags of Cheetos is approximately Normal with mean =5.09 ounces and standard deviation = 0.06 ounce. Draw an accurate sketch of the distribution of Cheetos bag weights. Be sure to label the mean, as well as the points one, two, and three standard deviations away from the mean on the horizontal axis. a) What percent of bags weigh less than 4.97 ounces? b) Between what weights do the middle 68% of bags fall? c) What percent of 5 ounce bags Cheetos weight between 5.03 and 5.21 ounces? d) A bag that weighs 5.15 ounces is at what percentile in this distribution?

9 Put a lid on It! At some fast-food restaurants, customers who want a lid for their drinks get them from a large stack left near straws, napkins, and condiments. The lids are made with a small amount of flexibility so they can be stretched across the mouth of the cup and then snuggly secured. When lids are too small or too large, customers can get very frustrated, especially if they end up spilling their drinks. At one particular restaurant, large drink cups require lids with a diameter of between 3.95 and 4.05 inches. The restaurant s lid supplier claims that the diameter of their large lids follows a Normal distribution with mean 3.98 inches and standard deviation 0.02 inches. Assume the supplier s claim is true. a) What percent of large lids are too small to fit? Show your method. b) What percent of large lids are too big to fit? Show your method. C) Compare your answers to (a) and (b). Does it make sense for the lid manufacturer to try to make one of these values larger than the other? Why or Why not? The supplier is considering two changes to reduce the percent of its large-cup lids that are too small to less than 1%. One strategy is to adjust the mean diameter of its lids. Another option is to alter the production process, thereby decreasing the standard deviation of the lid diameters. a) If the standard deviation remains at = 0.02 inches, at what value should the supplier set the mean diameter of its large-cup lids to ensure that less than 1% are too small to fit? Show your method. b) If the mean diameters stays at =3.98 inches, what value of the standard deviation will result in less that 1% of lids that are too small to fit? Show your method. c) Which of the two options in (a) and (b) do you think is preferable? Justify your answer. Outliers The percent of the observations that are classified as outliers by the 1.5 X IQR rule is the same in any Normal distribution. What is the percent? Show your method clearly. Section Response and explanatory variables 2. Scatterplot 3. Positive and negative association 4. Correlation r Treating breast cancer Early on, the most common treatment for breast cancer was removal of the breast. It is now usual to remove only the tumor and nearby lymph nodes, followed by radiation. The change in policy was due to a large medical experiment that compared the two treatments. Some breast cancer

10 patients, chosen at random, were given one or the other treatment. The patients were closely followed to see how long they lived following surgery. What are the explanatory and response variables? Are they categorical or quantitative? Rank the correlation Consider each of the following relationships: the heights of fathers and the heights of their adult sons, the heights of husbands and the heights of their wives, and the heights of women at age 4 and their heights at age 18. Rank the correlations between these pairs of variables from highest to lowest. Explain your reasoning. Teaching and research A college newspaper interviews a psychologist about student rating of the teaching of faculty members. The psychologist says, The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero. The paper reports this as Professor McDaniel said that good researchers tend to be poor teachers, and vice versa. Explain why the paper s report is wrong. Write a statement in plain language (don t use the word correlation ) to explain the psychologist s meaning. Section Regression line 2. Predicted value 3. Extrapolation 4. Residual 5. Least-squares regression line 5. Residual Plot 6. Standard deviation of the residuals 6. The coefficient of determination

11 Cars Car dealers across North America use the Red Book to help them determine the value of used cars that their customers trade in when purchasing new cars. The book lists on a monthly basis the amount paid at recent used/car auctions and indicates the values according to condition and optional features, but does not inform the dealers as to how odometer readings affect the trade-in value. In an experiment to determine whether the odometer reading should be included, ten 3- year old cars are randomly selected of the same make, condition, and options. The trade-in value and mileage are shown below. Trade in value (in 100s) Odometer (in 1000s) a. Sketch the scatterplot of this data.

12 b. Determine the least-squares regression line (LSRL) c. Provide an interpretation of the slope of this line in the context of these data. d. Calculate and plot ( x, y ) and graph it in the scatterplot. What do you notice about this point? e. Find the correlation coefficient for the relationship. Interpret this number. f. Find the coefficient of determination for the relationship. Interpret this number. g. Predict the trade-in value of a car with 60,000 miles. Earthquake Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Magnitude Depth(km) a) What is your explanatory variable? b) Sketch a scatterplot of the data. Find the correlation coefficient and the LSRL. c) How effective is the depth below the surface at which the quake occurs to predict the magnitude of an earthquake? Support your answer statistically.

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