mth 243 take-at-home midterm exam

• Work at your own pace in a quiet place
• Take breaks as needed
• Write or type your responses clearly—your thinking and your process should be clear to me (Ralf)
• If you have any questions, contact me as soon as possible

1. An opinion poll contacts 1667 adults in the USA and asks them, “Which political party do you think has better ideas for leading the country in the 21st century?” The choices for response are Democratic, Republican, Constitution, Green, Libertarian, or no party. Pollsters also asked if respondents had participated in 1, 2, 3, 4, or 5 of the last five elections.

Identify the:

1. population of interest
2. sample
3. variable(s) of interest, stating whether each variable is categorical, categorical ordinal, numerical continuous, or numerical discrete.

2. Identify the sampling method used for each survey below, and briefly explain your choices.
   1. To preserve binary gender representation, PCC randomly selects 54 female and 46 male PCC students for a survey about food and housing.
   2. A question posted on a website asks visitors their opinion on prison sentencing guidelines.
   3. A campaign director randomly selects one block from each of the city’s election districts. Campaign staff go to each block and interview all of its residents to determine which issues are most important to each district’s voters.

3. In a study of three nationally representative large-scale data sets from Ireland, the United States, and the United Kingdom (n = 17,247), teenagers between the ages of 12 to 15 were asked to keep a diary of their screen time and answer questions about how they felt or acted.

The answers to these questions were then used to compute a psychological well-being score. Additional data were collected and included in the analysis, such as each child’s sex and age, and on the mother’s education, ethnicity, psychological distress, and employment.

The study concluded that there is little clear-cut evidence that screen time decreases adolescent well-being.

1. What type of study is this?
2. Identify the explanatory variables.
3. Identify the response variable.
4. Can the results of the study be generalized to the population of Irish, USA, and UK teenagers? Why or why not?
5. Can the results of the study can be used to determine if screen time affects adolescent well-being? Why or why not?

4. Water samples from a certain river in North Carolina were taken at 16 different locations and tested for lead. Here are the data:

1. If the lead contamination level goal is 0.00 mg/L, what percentage of these river locations need decontamination work?
2. Use technology to make a histogram of the lead data. Use bins of width 0.05 starting at 0.00. Either paste your histogram into your work or sketch it carefully (whichever works better for you.)
3. Is the distribution unimodal, bimodal, multimodal, or uniform?
4. Is the distribution symmetric, skewed right, or skewed left?

5. Use technology to compute summary statistics (mean, SD, and five number summary) for the lead levels data from problem 4.
   1. What lead level is the 50th percentile?
   2. What’s the average lead level?
   3. On average, how far are the lead levels from the mean lead level?
   4. What is these lead levels’ interquartile range?

6. Here a stem-and-leaf display for course grades of an algebra class:

0 | 79 

1 | 

2 | 

3 | 2 

4 |

5 | 38

6 | 3679 ‘‘7 | 0’’ means 70

7 | 001389

8 | 03466789

9 | 011257

1. How many students earned Bs (course grades from 80 to 89)?
2. Which value is greater: the mean or the median? How do you know?
3. How many students would you estimate stopped participating in the class during the quarter? In the plot, what are their course grades called?

7. Scyrine and Alexandra are basketball players. The team statistician recorded the points each had scored in their first 20 games of the season, computed the five-number summaries, and made box plots for both players.

1. Describe similarities and differences of the players’ scoring abilities based on the statistics and boxplots. Be sure to compare both center and spread.
2. If you were the coach and you had to decide who would play in the state championship, which player would you choose and why? Justify your response using statistics.

8. An investigation compiled information about recent nonmilitary plane crashes. The causes that could be determined are summarized in the table below.

Cause Percent 

Pilot error 40% 

Other human error 5% 

Weather 6% 

Mechanical failure 14% 

Sabotage 6%

1. If the investigators were able to determine the causes of 625 plane crashes, how many of the crashes were caused by mechanical failure?
2. What percentage of the crashes were not determined?
3. Use a spreadsheet (like Google Sheets or Excel) to make a relative frequency bar plot for these data. Be sure to include a bar for crashes whose cause was “Not Determined.”

9. A survey of autos parked at a large university classified the brands by country of origin, as seen in the table.

1. What percent of the staff owned Asian cars?
2. What percent of Asian cars were owned by staff?
3. Use a spreadsheet (like Google Sheets or Excel) to make a stacked bar plot of these two variables.

10. A random sample of registered voters nationally were asked whether they think it’s better to raise taxes on the rich or raise taxes on the poor. The survey also collected information on the political party affiliation of the respondents. Here’s a mosaic plot of the data.

Based on the mosaic plot,

1. Which political party’s voters are least likely to support raising taxes on the rich?
2. Which political party’s voters are least likely to support raising taxes on the poor?
3. Do views on raising taxes and political affiliation appear to be independent? Explain your reasoning.