12002 AP Statistics Exam Multiple Choice Solutions 1. Answer: (D) (A)is FALSE → There are not necessarily more subjects available for either experiments or observational studies. There are probably more subjects available for observational studies if anything because people are more apt to be alright with someone observing them than to take place in an experiment. (B)is FALSE → In anything, ethical constraints might prevent certain large scale experimentsfrom taking place, not observational studies. (C)is FALSE → On average, experiments tend to be more costly than observational studies. (D)is TRUE → Only through a well-designed experiment can we determine a causal relationship between our variables whereby in an observational study, we can only determine if there is an association between our variables. (E)is FALSE → You can do significance tests on any data, whether it comes from an observational study or an experiment. 2. Answer: (B) Choices (A) and (E) are out from the get-go because the null hypothesis must have p = 0.05 in it. Since we are checking to see if the manufacturer is wrong (and the manufacturer says that it is “no more than 0.05”), we must be testing for the idea that the proportion is morethan 5% or Ha: p > 0.05. Note: Our parameter of interest in this example is p, the true proportion of balloons that burst when inflated to a diameter above 12 inches. This is because this is categorical data...the balloons either burst or don’t. 3. Answer: (C) If you want to see how these Lauren performed in a relative sense and the scores follow a normaldistribution, then you may use z scores: 1st exam: 1107585=−=−=σμxz2nd exam: 1157085=−=−=σμxzSince the z scores are the same [both times she scored exactly one standard deviation above the rest of the class], she scored about equally as well on both exams. The class size and correlation between the two scores is irrelevant for this question. www.mymathscloud.com
24. Answer: (A) Recall that when you are setting up a simulation you must disregard the values of the numbersand simply treat them as non-numerical objects. Since 30% of all subscribers watch the shopping channel at least once a week, make 30% of the 10 numbers represent those people and the other 70% of the 10 numbers represent the other people. The numbers do not represent quantities, they only represent outcomes. 5. Answer: (D) There are a couple different ways you can do this: Method 1: Figure out the expected number of sweatshirts that are sold: ()()()()()()()52.102.0508.041.033.022.013.00)(=∗+∗+∗+∗+∗+∗===∑iixpxxEμNow since each sweatshirt is sold for $25, they should expect to make: $25 × 1.52 = $38 Method 2: Convert the original data from number of sweatshirts to amount of money earned: Money per sweatshirt x$0 $25 $50 $75 $100 $125 P(x) 0.3 0.2 0.3 0.1 0.08 0.02 Now do the same thing to find the expected revenue:()()()()()()00.38$02.012508.01001.0753.0502.0253.00)(=∗+∗+∗+∗+∗+∗=xEKeep in mind, though, that you don’t have to do these by hand unless it’s a free response question, and even then you need only show the formulas for the purpose of presentation. If it’s a multiple choice question like this, just do it in the calculator: www.mymathscloud.com
31. Press STAT and press ENTER. 2. Enter all the x values into L1 and all the probabilities into L23. Press STAT→CALC→1-Var-Stats3. Now tell it to do 1-Var Stats on L1 with a frequency of L2.4. Press ENTER and thexis your mean (expected value) and xσ is your standard deviation. 4. You can also do this from the perspective of money... same exact process. 6. Answer: (E) Recall that the correlation coefficient (r) is not affected by multiplying, adding, subtracting, or dividing (any linear transformation does not affect the correlation coefficient). The only thing that could affect the correlation coefficient was if you were to do some sort of non-linear transformation such as taking the log, taking the square root, or squaring every data value. So it remains the same. www.mymathscloud.com
