AP Statistics / Mr. Hansen |
Name: __________________________ |

Additional Study Questions for Midterm Exam

(**NOT** a comprehensive list of questions)

**Instructions:** You may use your graphing calculator throughout. In keeping with AP standards, the following rules apply:

- If you make an error, you may save time by crossing it out rather than trying to erase it. Erased or crossed-out work will not be graded.
- Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as the accuracy of your final answers. Correct answers without supporting work may not receive credit. Justifications require mathematical (noncalculator) reasons.
- You are permitted to use your calculator to perform computations and to check your work in any manner that you wish. However, you must clearly indicate the setup of your problem, namely the formula or equation you are using. Even if your calculator contains a program or built-in procedure for finding a result (e.g., finding the mean of a random variable), you must indicate step-by-step how you are computing your result.
**Correct answers without supporting work may receive no credit.** - Your work must be expressed in standard mathematical notation, not calculator syntax. For example, the normal probability
*P*(*Z*> 2.3) may not be written as normalcdf(2.3,99999,m,s). - Unless otherwise specified, give answers in simplified exact form (fraction or numeric). If a decimal approximation is requested, give the final answer correct to at least three places after the decimal point unless otherwise specified.

**List of Terms.** You may find the following list of terms useful, especially in places where you are required to fill in a blank. However, it is not necessarily the case that every blank can be filled by an entry from this list.

addition rule for means and variances |
independent events |
response (or nonresponse) bias |

anecdotal evidence |
independent random variables |
response variable |

bar graph / segmented bar graph |
influential observation for regression |
sample mean |

bias |
IQR |
sample proportion |

blind test / double-blind test |
law of large numbers |
sample space |

blocking (block design) |
least-squares regression |
sampling |

boxplot |
level |
scatterplot |

case |
lurking variable(s) |
Simpson’s paradox |

categorical variable |
matching / matched pairs |
simulation |

census |
mean |
skew left, skew right |

clustering |
mean of a random variable |
SRS |

combinations ( |
median |
standard deviation |

common response |
mode |
standard deviation of a random variable |

complement rule |
multiplication rule |
statistic |

conditional probability |
normal quantile plot |
statistical inference (3 principles): |

confounding |
outcome |
1. controlling the variables |

continuous random variable |
outlier |
2. randomization |

control group |
parameter |
3. replication |

correlation coefficient |
permutations ( |
statistical significance |

correlation vs. causation |
placebo effect |
stemplot |

discrete random variable |
population mean |
strata |

disjoint events |
population proportion |
stratified random sample |

event |
probability |
subject |

expected value |
probability distribution |
symmetric |

experiment |
prospective study |
time series |

explanatory variable |
quantitative variable |
transformations to achieve linearity |

exploratory data analysis |
quartiles (Q1, Q3) |
tree diagram |

exponential growth |
random variable |
two-way / three-way table |

factor |
range |
unbiased estimator |

gaps |
residual |
variance |

histogram |
residual plot |
variance of a random variable |

**Formulas.** Because the AP exam does not require you to memorize many formulas, standard formulas (e.g., mean, conditional probability, etc.) will be furnished for you. You will also receive a normal probability table and a table of random digits.

Part I: Fill in the Blank

1. Although human judgment is better, the "1.5 IQR" rule is useful in cases where automated determination of ______________ is needed.

2. In a symmetric distribution, the mean equals the median. However, in a ______________ distribution, the mean is pulled significantly to the left of the median.

3. The range, IQR, variance, and standard deviation [fill in **are **

4-5. The values and *s* are examples of ______________ , while *µ* and s are examples of ______________ .

6-7. Because human subjects (as well as researchers) are easily swayed into seeing positive results from experimental treatments (a phenomenon known as the ______________ ), it is crucial that any scientifically valid experiment include a ______________ that receives no actual treatment.

8. Measurements of a variable taken at regular time intervals are called a ______________ .

9. State *both* of the two equivalent tests for checking whether non-null events A and B are independent: __________________________________ , __________________________________

10. The term *probability* means _________________________________ . The AP graders [fill in **do **

11. A scientific poll published in *The Washington Psssst* reports that 52% of Americans, with a margin of error of 3%, believe that their hometown has been visited by extraterrestrial creatures. (If the confidence level is not specified, we are to assume _____ %.) Explain, using approved wording, what this means concerning the true population proportion of Americans who believe this astonishing statement. __________________________________________________________________________

Part II: Problem Solving

12. The Wonder Water Fishing Hole is known far and wide for the quality of the fish in its amply stocked pond. Recently a researcher made a study of the weight of fish caught and the age of each fish (computed based on tagging data stored in a central computer). A representative subset of the data (shown below) might make a tempting regression study.

Age (days) |
Weight (ounces) |

90 |
72 |

70 |
77 |

45 |
65 |

75 |
69 |

75 |
70 |

50 |
65 |

135 |
62 |

70 |
71 |

(a). First, code the weights as weights in excess of 50 ounces. Show a boxplot of the coded weights.

(b) Compute the five-number summary for the coded weight data. No need to show work.

(c) Compute the standard deviation of the coded weight data. No need to show work.

(d). Now, let us consider the role of the other column of data (the ages). If we are writing an article for an anglers’ journal, we might want to be able to predict fish weight based on ages. What would be the explanatory variable? ______________________ What would be the response variable? _____________________

(e) Create a scatterplot and a suitable regression line that we might be able to use as a way of predicting fish weight. Draw your scatterplot and regression line here.

(f). What is the slope of your regression line from part (e)? ___________________________

(g) Compute and draw the residual plot for this regression model. Is the linear model a good fit to the data over the domain seen? Explain your answer.

(h) In our article for *Fishing Times,* what would be a reasonable estimate of the weight of a 70-day-old fish? **Show your work. **(Yes, your calculator can find the answer in a jiffy, but show your work anyway.)

(i). Would it be reasonable to use your regression line to estimate the weight of a 30-day-old fish? Why or why not?