Learn Extracted exam questions AP Statistics 2016 Free Response
2016 Free Response
Source PDF on the left, extracted YAML on the right. Compare numbering, marks, options and text.
Robin works as a server in a small restaurant, where she can earn a tip (extra money) from each customer she serves. The histogram below shows the distribution of her 60 tip amounts for one day of work.
[Histogram titled "Number of Tips" (y-axis, 0 to 25) vs. "Tip Amounts (dollars)" (x-axis, 0 to 20+). Bars: 0-5 dollars = 25 tips; 5-10 dollars = 22 tips; 10-15 dollars (first bin) = 6 tips; next bin = 4 tips; next two bins = 1 tip each; a bar near 20+ dollars = 1 tip. (Bin boundaries approximate; bar heights labeled directly on histogram: 25, 22, 6, 4, 1, 1, 1.)]
Write a few sentences to describe the distribution of tip amounts for the day shown.
One of the tip amounts was $8. If the $8 tip had been $18, what effect would the increase have had on the following statistics? Justify your answers.
The mean:
The median:
Product advertisers studied the effects of television ads on children's choices for two new snacks. The advertisers used two 30-second television ads in an experiment. One ad was for a new sugary snack called Choco-Zuties, and the other ad was for a new healthy snack called Apple-Zuties.
For the experiment, 75 children were randomly assigned to one of three groups, A, B, or C. Each child individually watched a 30-minute television program that was interrupted for 5 minutes of advertising. The advertising was the same for each group with the following exceptions.
- The advertising for group A included the Choco-Zuties ad but not the Apple-Zuties ad.
- The advertising for group B included the Apple-Zuties ad but not the Choco-Zuties ad.
- The advertising for group C included neither the Choco-Zuties ad nor the Apple-Zuties ad.
After the program, the children were offered a choice between the two snacks. The table below summarizes their choices.
| Group | Type of Ad | Number Who Chose Choco-Zuties | Number Who Chose Apple-Zuties |
|---|---|---|---|
| A | Choco-Zuties only | 21 | 4 |
| B | Apple-Zuties only | 13 | 12 |
| C | Neither | 22 | 3 |
Do the data provide convincing statistical evidence that there is an association between type of ad and children's choice of snack among all children similar to those who participated in the experiment?
Write a few sentences describing the effect of each ad on children's choice of snack.
Alzheimer's disease results in a loss of cognitive ability beyond what is expected with typical aging. A local newspaper published an article with the following headline.
"Study Finds Strong Association Between Smoking and Alzheimer's"
The article reported that a study tracked the medical histories of 21,123 men and women for 23 years. The article stated that, for those who smoked at least two packs of cigarettes a day, the risk of developing Alzheimer's disease was 2.57 times the risk for those who did not smoke.
Identify the explanatory and response variables in the study.
Explanatory variable:
Response variable:
Is the study described in the article an observational study or an experiment? Explain.
Exercise status (regular weekly exercise versus no regular weekly exercise) was mentioned in the article as a possible confounding variable. Explain how exercise status could be a confounding variable in the study.
A company manufactures model rockets that require igniters to launch. Once an igniter is used to launch a rocket, the igniter cannot be reused. Sometimes an igniter fails to operate correctly, and the rocket does not launch. The company estimates that the overall failure rate, defined as the percent of all igniters that fail to operate correctly, is 15 percent.
A company engineer develops a new igniter, called the super igniter, with the intent of lowering the failure rate. To test the performance of the super igniters, the engineer uses the following process.
Step 1: One super igniter is selected at random and used in a rocket.
Step 2: If the rocket launches, another super igniter is selected at random and used in a rocket.
Step 2 is repeated until the process stops. The process stops when a super igniter fails to operate correctly or 32 super igniters have successfully launched rockets, whichever comes first. Assume that super igniter failures are independent.
If the failure rate of the super igniters is 15 percent, what is the probability that the first 30 super igniters selected using the testing process successfully launch rockets?
Given that the first 30 super igniters successfully launch rockets, what is the probability that the first failure occurs on the thirty-first or the thirty-second super igniter tested if the failure rate of the super igniters is 15 percent?
Given that the first 30 super igniters successfully launch rockets, is it reasonable to believe that the failure rate of the super igniters is less than 15 percent? Explain.
A polling agency showed the following two statements to a random sample of 1,048 adults in the United States.
Environment statement: Protection of the environment should be given priority over economic growth.
Economy statement: Economic growth should be given priority over protection of the environment.
The order in which the statements were shown was randomly selected for each person in the sample. After reading the statements, each person was asked to choose the statement that was most consistent with his or her opinion. The results are shown in the table.
| Environment Statement | Economy Statement | No Preference | |
|---|---|---|---|
| Percent of sample | 58% | 37% | 5% |
Assume the conditions for inference have been met. Construct and interpret a 95 percent confidence interval for the proportion of all adults in the United States who would have chosen the economy statement.
One of the conditions for inference that was met is that the number who chose the economy statement and the number who did not choose the economy statement are both greater than 10. Explain why it is necessary to satisfy that condition.
A suggestion was made to use a two-sample $z$-interval for a difference between proportions to investigate whether the difference in proportions between adults in the United States who would have chosen the environment statement and adults in the United States who would have chosen the economy statement is statistically significant. Is the two-sample $z$-interval for a difference between proportions an appropriate procedure to investigate the difference? Justify your answer.
A newspaper in Germany reported that the more semesters needed to complete an academic program at the university, the greater the starting salary in the first year of a job. The report was based on a study that used a random sample of 24 people who had recently completed an academic program and were selected to represent the population of that country, in thousands of euros, for the first year of a job. The data are shown in the scatterplot below.
[Scatterplot titled with y-axis "Starting Salary (1,000 euros)" ranging approximately 25 to 65, x-axis "Number of Semesters" ranging approximately 0 to 20. Points scattered showing a general upward trend from lower-left (fewer semesters, lower salary, around 30) to upper-right (more semesters, higher salary, up to about 65), with considerable scatter throughout.]
The table below shows computer output from a linear regression analysis on the data.
| Predictor | Coef | SE Coef | T | P |
|---|---|---|---|---|
| Constant | 34.018 | 4.455 | 7.64 | 0.000 |
| Semesters | 1.1594 | 0.3482 | 3.33 | 0.003 |
$S = 7.37702$ $R\text{-Sq} = 33.5\%$ $R\text{-Sq(adj)} = 30.5\%$
Does the scatterplot support the newspaper's report about number of semesters and starting salary? Justify your answer.
Identify the slope of the least-squares regression line, and interpret the slope in context.
An independent researcher received the data from the newspaper and conducted a new analysis by separating the data into three groups based on the major of each person. A revised scatterplot identifying the major of each person is shown below.
[Revised scatterplot, same axes as before (y-axis "Starting Salary (1,000 euros)" approximately 25 to 65, x-axis "Number of Semesters" approximately 5 to 20), with points marked by three different symbols per the legend "Major: Business (square), Physics (circle), Chemistry (diamond)". Business-major points cluster at lower semesters with lower-to-moderate salaries; Physics- and Chemistry-major points spread across higher semesters with a range of salaries, generally higher for more semesters.]
Based on the people in the sample, describe the association between starting salary and number of semesters for the business majors.
Based on the people in the sample, compare the median starting salaries for the three majors.
Based on the analysis conducted by the independent researcher, how should the newspaper report be modified to give a better description of the relationship between the number of semesters and the starting salary for the people in the sample?