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1) Lucas is writing an article about the baseball teams for the school paper. He collects data about each player's position, batting average, number of at-bats, hits, stolen bases and whether each player is on the junior varsity or varsity team. Who are the individuals? Which variables are categorical? Which are numerical?
2) Malia has been put in charge of analyzing the employees at her company. She collects information regarding annual salary, years with the company, highest degree earned, job title, yearly contribution toward 401K, number of children, home address and phone number. Who are the individuals? Which variables are categorical? Which are numerical?
3) Determine whether each of the following variables is categorical or numerical.
a) The heights of all of the volleyball players.
b) The position played by all of the football players.
c) The brand of mascara preferred by those surveyed.
d) The numbers of texts sent per month.
e) Each person's social security number.
f) Each person's cell phone provider.
4) The fourth graders at Sand Creek Elementary are doing a unit on weather. There is a thermometer on the building just outside the classroom window. The students will record and analyze the temperature at 8:00 a.m. and 2:00 p.m. every school day for 5 weeks, and then create a graph and write a report based on their findings.
a) Identify the variable of interest, the instrument used, and the units.
b) Comment on the validity, reliability and potential bias for this study.
5) The first graders at Sand Creek Elementary are doing a unit on measurement. Each student has traced her or his own foot and cut it out. Each student will use his or her 'foot' to measure various objects around the room and school. Some of the measurements they will make are height of self and at least two other friends, width of the classroom door, length of a lunch table, etc.
a) The variables of interest are the lengths, widths and heights of various objects. Identify the instrument used, and the units.
b) Comment on the validity, reliability, and potential bias for this study.
6) Determine whether each of the following measurements would have a problem with any of the following: VALIDITY (problem would be a lack of), RELIABILITY (problem would be a lack of), BIAS, (problem would be the presence of). A measurement may have any combination of the factors. For each one with a problem, suggest a better way to make the measurement. (hint: answer similar to example #2)
a) A speedometer is totally unpredictable.
b) Cholesterol levels are determined by patients filling out a survey regarding their diet.
c) Time is measured by using the clock on a cell phone.
d) Grades in a Physics class are determined by students assessing themselves on a scale of 1 to 10.
e) Grades in a statistics class are determined by students' scores on one cumulative test.
f) Sobriety is determined by a breathalyzer that is calibrated to be too sensitive.
7) Super Duper High School has a total of 143 teachers. Suppose that you are a researcher who is interested in studying Teacher Effectiveness at SDHS. You intend to evaluate the effectiveness of all of the teachers for your report.
a) What type of data collection method is this?
b) Suggest at least two valid variables that you might study. Include an instrument that can be used to measure your variables and the units.
c) Suggest at least two invalid variables that you might study. Include an instrument that can be used to measure your variables and the units.
8) For each of the following scenarios, determine whether the situation described is an experiment, observational study, census, or a sample survey. Explain how you know.
a) The Super Spaz Energy drink company randomly selects 2% of the cans filled each day, and tests them for volume, ingredient content, and taste.
b) A government lobbyist analyzes the crime reports for the 4 counties in her community.
c) New advertisements are generally tried out on focus groups before investing a lot of money to pay for airtime on national TV.
d) Each student in Probability and Statistics will take the District Common Assessment as a final exam.
e) A teenager decides to evaluate how serious her parents are about her curfew by coming home 15 minutes late just to see what happens.
9) Pasquale's Big and Tall Shop sold 127 suits during the first quarter of this year, and 17 were returned. Marco's XXL Shop sold 268 suits during the same time period, and 27 were returned.
a) What were the number of returns for each shop? Which shop had a higher number of returns?
b) What were the rates of returns for each shop? Which shop had a higher rate of returns?
c) Which of these statistics gives a more clear representation of customer satisfaction? Explain.
Review Exercises
10) Jolene makes $12.45 per hour at her job. Last year she made $10.85. What percent of a raise did Jolene receive?
11) Michaela’s favorite shoes are normally $42.99. Today she found a sale in which they were marked down to $27.99. What percent of a discount is this?
12) The number of incidents of hazing reported at Some Random High School was 84 during the 2010-2011 school year. The following year there were 37 incidents of hazing reported at SRHS. What is the rate of change in reported hazing incidents between these two school years? Is it an increase or a decrease?
13) SRHS has had a huge problem getting students to class on time, so the administrators have implemented a new tardy policy. In an effort to determine whether or not it is working to deter students from being tardy to class, data has been collected and analyzed. The following table shows some of the data:
[Figure4]
a) Calculate the percent of change for each category and complete the table (round to the nearest tenth of a percent).
b) Which category saw the most significant change?
c) Based on these calculations, do you feel that the tardy policy is working? Explain your reasoning.
Image Attributions
Image Attributions
- [1]^ License: CC BY-NC 3.0
- [2]^ License: CC BY-NC 3.0
- [3]^ License: CC BY-NC 3.0
- [4]^ License: CC BY-NC 3.0
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