Midterm Exam Stuff

Let's take this midterm exam as seriously as we intend to take our AP exams; this is a great opportunity to take a shortened practice test and really gauge our progress in preparing for the big day, May 17th. Work hard leading up to the exam and do your best--that's all I ask for, but who cares about me--that's what you should demand of yourself!

If you did not turn in your stamps you must turn them in during exams! Don't get a 0!

Here is a breakdown of the midterm exam:

• Multiple Choice Section
• 60 minutes
• 50% of midterm exam score
• 28 questions
• Free Response Section
• 60 minutes
• 50% of midterm exam score
• 5 questions
• 1 FR: Experimental design (discussed in class)
• 1 FR: Probability 
• 1 FR: Creating Graphical Displays and Summarizing/Comparing Distributions
• 1 FR: Linear Regression
• 1 FR: Use a given graphical display (that you have not necessarily seen) to analyze a context and draw conclusions
• Take a look at FR #1 of the 2015 midterm that was emailed to you
• This type of graph is not on our midterm, but this question challenges you to examine a new type of graphical display and use it to draw conclusions about a context--you will have a similar style question on your midterm

Here are the answer keys for the additional resources provided in class; hints are also provided, as well as some information about the midterm...

USE THIS STUFF! Practice, practice, practice! Also work on the 2015 Midterm that was emailed to you, it's another great resource!

• AP Statistics Midterm Exam: Multiple Choice Extension Questions (hints provided)
• 1.) E
• First, use P(D and E) = .018 and the fact that P(D) = 0.6 to find P(E).
• Then, calculate P(D) or P(E) using this answer
• There are questions calculating "AND" and "OR" type probabilities on the midterm, but entirely in context--there is not a question that is this purely formulaic
• 2.) C
• Which part of the normal model contains the "most" data values? 
• The center is the highest part of the curve, and thus contains the most data--so the interval that contains the greatest proportion will centered around the mean
• OR....
• The "proportion of cartons of large eggs at the store" for each interval would be calculated using normalcdf, but we would need to know the standard deviation to use this--a standard deviation is not given, but we can make one up and use it to test each MC option! 
• I assumed standard deviation = 1 and then used normalcdf to find the proportion of cartons in each interval (a. 0.0228; b. 0.49997; c. 0.9545; d.) 0.4999; e.) 0.0228)
• Be sure to have an understanding of the Normal model for your midterm!
• Know how to use normalcdf to find percentages/probabilities for a Normal model
• Know how to use invnorm( to find data values that represent a given percentile
• Remember how to combine random variables to find a new mean and standard deviation--and then we can apply the Normal model using these values (see #3)
• 3.) B
• First, find the mean, based on rescaling, for 5X - 10Y
• Second, find the standard deviation, based on rescaling, for "5X"
• Now, find the standard deviation, based on rescaling, for "10Y"
• Now, use the idea that "variances always add" to find the standard deviation for 5X - 10Y
• *Note: The "A players total points are calculated as follows: 5X - 10Y" information was not provided in the original question. Examine this expression and re-read the context--how do we arrive at this expression?
• 4.) A
• This question is all about reading carefully
• I would recommend first finding the range for each and using this to narrow down your options
• You can then calculate the median for each (by hand or using your graphing calculator) to decided between A and D
• You may also be able to look at the graph and visually determine that the distribution for females is centered around a higher value
• *You will have to create back to back stemplots the free response section of your midterm
• 5.)  D
• To find the weight, in pounds, at the 75th percentile we could use invnorm(area, mean, st. dev.); next we can see which MC option/expression roughly equals this value
• OR...
• This invnorm( calculation is really based on the z score...
• We know the mean and standard deviation, so if we can figure out what z-score marks the 75th percentile we can substitute that z-score, mean, and standard deviation into the z-score formula and "solve for x"
• This is what our calculator is doing with invnorm(
• To find the z score that marks the 75th percentile we could use a z-table, or we could use invnorm again
• invnorm(0.75, 0, 1)
• .75 is the area to the left or percentile, 0 represents the mean for z-scores, and 1 represents the standard deviation for z-scores
• 6.) E
• Calculate the fences! Check your notes
• And remember, there could still be data values between Q3 and the Max, we just don't know what they are....we don't have that information
• 7.) D
• I used normalcdf( to find the percentile for Aliyaah's height
• We know that the z-score for Aaliyah's height is 0.96 (z-score = the distance from the mean measured in standard deviations)
• So, we'll have to enter a z-score into normalcdf, which means we'll use 0 and 1 for the mean and standard deviation
• We want her percentile, which means we would "shade to the left" if we sketch the model
• normalcdf(-9999999, 0.96, 0, 1) = 0.83
• Now we have each percentile, and we know that Aliyaah is at a lower percentile, which means she is shorter
• 8.) B
• 9.) D
• The median is the middle number--we know each data set has 28 values, and so we know the median is between the 14th and 15th data values (28/2 = 14, median between 14th, 15th data values)
• We can then "count the dots" to find were the 14th/15th data values fall
• We can use the same strategy for Q1 and Q3 (and so, IQR)
• Q1 is the first quartile, so this would be roughly the 7th data value (think: one fourth of 28)
• Q3 is the third quartile, so this would roughly be the 21st data value 
• *Challenge: if Q1 is the same for each, could Q3 be different for this multiple choice question? Why or why not?
• Calculate the range for each
• 10.) D
• We block based on a specific characteristic, like "by the river" and "by the woods," or "room with view" and "no view." 
• We then randomly assign treatments within these blocks
• 11.) A
• Be sure to know what each of our summary statistics actually measures! 
• AP MC WU
• 1.) A
• You could use a tree diagram here
• OR, consider "using words" and substituting probabilities--if people call in sick that means "sunny and call out sick given sunny" OR "not sunny and call out sick given not sunny"
• 2.) C
• Know how mean and median compare based on the shape of a distribution (check your notes!)
• 3.) D
• We can use a Venn diagram or the general addition rule here
• "At least one of the two places" means the person visited the park only, the cave only, or both.
• 4.) E
• Look back at your notes/examples about comparing boxplots!
• AP Stat: Midterm Exam Review (Stamp!)
• 21.) C
• "regression line is an appropriate model"--remember, we want the residual plot to show random scatter
• There are two other conditions to check to determine if a linear model is appropriate--what are they?
• What does a residual plot show us? How could we create residual plot given the original scatterplot and LSRL? How could we re-create the distribution of the points around the LSRL in the original graph given only the residual plot?
• This idea shows up on your midterm!
• Influential Point Question: C
• Check your notes from chapter 9 about outliers, leverage, and influence!
• We have lots of examples like this
• 32a.) predicted final exam score = 63.328 + 2.697(study hours)
• Remember to use a "hat" to show "predicted"
• 32b.) r = 0.753
• Find r from R^2!!
• Always remember to check the slope to determine if r is + or -
• Be sure you know how to do each of the things mentioned in the "Extra Review" list (for regression)!
• Most of these topics appear on your midterm exam, some on the MC, some on the FR
• The World Almanac and Book of Facts Question:
• Should any states be considered outliers? Yes, there is at least one outlier, the maximum of 25.8.
• Calculate the fences! Check your notes!
• Fences = 1.95 and 25.55
• This came up twice in all this review? Must be on the midterm....
• Measures of Center provided: mean, median
• Measures of Spread: standard deviation (IQR, Range can be calculated from the info given)
• Know about the measures of center and spread, and be sure you know how to use "SOCS" to describe a distribution or compare two distributions--this is on the midterm!
• Shape: skewed right 
• Here, the mean greater than the median....
• Know how the mean and median relate based on the shape of a distribution
• Know how measures of center and spread are or are not affected by outliers
• Which measures of center/spread are sensitive to extremes?
• Which are resistant to extremes?
• AP Free Response #1: Comparing Boxplots
• Sample Responses:
• a.) The distributions for the percents of seniors who took the college entrance exam appears roughly symmetric for region I an skewed right for Region II. Region II has one high outlier around 30%, while Region I does not have any outliers. Region I has a much higher median percent of seniors to took the college entrance exam. Region I has a wider IQR and a larger range if we exclude the outlier in Region II, which suggests Region I showed more variability in its percentages (aside from the outlier). Generally, a higher percentage of seniors in Region I took the college entrance exam; in region I, all high schools were above 60%, while in region II only one school was above 15%.  
• You will have to compare two distributions on the midterm exam! Be ready for this!
• First you will have to create the graphical display to use for your comparison: be sure you know how to make histograms, boxplots, and stemplots!
• b.) The histogram of the combined data would be bimodal, with a cluster of data between 0 and 15% (Region I) and another cluster around 60-90% (Region II). There would only be one data value (the outlier in Region I) roughly between 20 and 60%.
• Scoring Rubric:

• AP Stat Mini Test: Geometric and Binomial Probability (from the Friday before winter break)
• 1a.) 0.90
• 1b.) 0.99999
• 1c.) 0.0729
• 1d.) 0.032
• 1e.) P(Sam receives more than 20 flights) = 0.00137
• *Be sure to answer the question and in context! Many people simply provided a number, which is not sufficient
• When taking the midterm exam always re-read the question--and make sure you answered it, in context!
• Midterm Exam Tip: Try to take the wording of the context right out of the given question/info
• Reword the given questions and context to start your responses!
• "I would be surprised if Sam receives more than 20 upgrades because the probability of this occurring is very low.
• OR... 
• "I would be surprised if Sam receives more than 20 upgrades because he is only expected to receive 10.4 upgrades during the year, on average.
• (This type of response would earn partially correct; we would also need to use/reference the standard deviation to complete this logic).
• 2.) B
• 3.) C
• 4.) D
• 5.) E
• 6.) A
• 7.) A
• 8.) B
• 9.) A
• 10.) B
• Experimental Multiple Choice: Experimental Design (went over 1-3 in class today)
• 1.) E
• 2.) E
• 3.) E
• 4.) D
• An experiment is the only method of data collection that allows us to establish a cause and effect relationship!
• 5.) D
• 6.) D
• 7.) D
• Experiments Wrap Up (provided today in class)












• AP Free Response on Midterm:
• Describe a method for randomly assigning treatments, or for randomly assigning treatments within blocks
• Identify factors, levels, treatments, response variable for an experiment
• 2015 Midterm: MC Key
• 1.) C
• 2.) A 
• 3.) E
• 4.) B
• 5.) B
• 6.) D
• 7.) D
• 8.) E
• 9.) D
• 10.) C or D (create a residual plot; if you think it has a pattern the answer is C, if you think this is random scatter it's D--this would be much more clear on our midterm, I stopped using this question for that reason)
• 11.) D
• 12.) D
• 13.) A
• 14.) D
• 15.) E
• 16.) E
• 17.) B
• 18.) B
• 19.) D
• 20.) C
• 21.) B
• 22.) C
• 23.) D
• 24.) D
• 25.) A
• 26.) C
• 27.) E
• I typed this fairly quickly so if you disagree with one of my answers send me a Remind and/or let me know if I made an error! (I don't think I did, but it's always possible!)

Check out the image below for some suggestions about how to study: