• What is the average of miles per gallon for all new motorcycles? According to reports, a random sample of 40 motorcycles gave an average of 38.2 mpg.
  • Identify the variable of interest.
  • Is this variable of interest quantitative or qualitative?
  • From what population was this sample selected?

2. Categorize each technique described below as simple random sampling, stratified sampling, systematic sampling, cluster sampling, or convenience sampling.

• To determine the average IQ of ninth-grade students, a school psychologist obtains a list of all high schools in the local public school system. She randomly selects five of these schools and administers an IQ test to all ninth-grade students at the selected schools.
• A member of Congress wishes to determine her county’s opinion regarding gay marriage. She divides her county into three income classes: low-income households, middle-income households, and upper-income households. She then takes a random sample of households from each income class and asks them their opinion.
• A radio station asks its listeners to call in their opinion regarding the use of American forces in peacekeeping missions.
• In an effort to identify whether an advertising campaign has been effective, a marketing firm conducts a nationwide poll by randomly selecting individuals from a list of known users of the product.
• A lobby has a list of the 100 senators of the U.S. In order to determine the Senate’s position regarding legalization of marijuana, they decide to talk with every seventh senator on the list starting with the third.

3. Which technique for gathering data (observational study or experiment) do you think was used in the following studies?

• Rats with a disease are given a drug thought to help fight the disease. Certain rats are given 5 mg of the drug each day, and other rats are given 10 mg of the drug each day. The rats are administered the drug for a one month period. After that month, scientists study how well the drug helped fight the disease.
• A poll is taken in which 500 randomly selected voters are asked who they will vote for in an upcoming election.
• A traffic safety officer parks near an intersection and measures how fast the next 100 drivers go through the intersection.
• One hundred obese children are asked to exercise one hour a day for one month. Once the month is over, researches measure the change in weight for these children.

4. Is college worth the expense? To answer this question, many different subjects are asked their average annual income. The average annual incomes (in thousands of dollars) from the sample are as follows: 18.3 if the students dropped out of high school, 32.5 for high school graduates, 49.5 for those with bachelor's degrees, 72.3 for those with master's, and 86.2 for those with doctoral degrees. Make a bar graph showing average annual income for each education level.

5. Below are the points scored by a college football team out of a sample of fourteen games played that season:

• Make a stem-and-leaf plot for this data.
• Calculate the sample mean for this data.
• Calculate the sample median for this data.
• According to the mean and median you just calculated, what would you expect the shape of this distribution to be?
• Calculate the range for this data.
• Calculate the sample standard deviation for this data.
• Find the three quartiles for this data.
• Find the interquartile range for this data.
• What plot would you use to represent these three quartiles?

6. In your chemistry class, suppose your final grade is based on a lab score, two major test scores, and a final exam score. There are 100 points available for each score. However, the lab score is worth 20% of your total grade, each major test is worth 25%, and the final exam is worth 30%. Compute the weighted average for the following scores: 91 on the lab, 83 on the first major test, 88 on the second major test, and 86 on the final exam.