1.7: Exercises

1. A study was conducted of schools across the U.S. about whether they require school uniforms. Two hundred ninety-six schools gave their response to the question, “Does your school require school uniforms?” State the population and sample.

2. The U.S. Department of Labor collects information on the average hourly earnings of professional and business services positions. Suppose that you look at 20 years, and collect data on the average hourly earnings in those years. State the population and sample.

3. A person collects the gas prices at 25 gas stations in Phoenix, AZ. State the population and sample.

4. The Center for Disease Control collects data on the number of children with autism. They collect data on 32,601 children in the state of Arizona, and then look to see how many have autism. State the population and sample.

5. Determine if the variable is qualitative or quantitative. If quantitative, then also state if the variable is discrete or continuous.

1. Height of buildings in a town
2. Eye color of all students at a college
3. Weight of cars
4. Number of dogs in a household
5. Religion of people in a town
6. Number of fish caught daily

6. Determine if the variable is qualitative or quantitative. If quantitative, then also state if the variable is discrete or continuous.

1. Letter grades of students in a class
2. Distance a person runs every day
3. Number of prairie dogs on a parcel of land
4. Time that a task takes to complete
5. Gender of a person
6. Number of cars at a dealership on a given day

7. A study to estimate the average salary of workers at a university was conducted using the following designs. Categorize the sampling method as a simple random sample, stratified sample, cluster sample, systematic sample, or convenience sample.

1. Each person who is employed by the university is first divided into groups of administrative professional, classified, faculty, and part-time. Then each person in those groupings is given a number and then random samples are taken inside each grouping.
2. Each researcher asks the first 40 people he or she encounters on campus what their salary is.
3. The researchers number all employees, and then start with the 34th person. Then they record the salary of every 10th person after that.
4. The researchers number all employees, and then use a random number generator to determine which employees they will use.
5. Each college on campus is given a number. Then five colleges are chosen at random and all employees’ salaries in each college is recorded.

8. A study to determine the opinion of Americans about the use of marijuana for medical purposes is being conducted using the following designs. Categorize the sampling method as a simple random sample, stratified sample, cluster sample, systematic sample, or convenience sample.

1. The researchers attend a festival in a town in Kansas and ask all the people they can what their opinions are.
2. The researchers divide Americans into groups based on the person’s race, and then take random samples from each group.
3. The researchers number all Americans and call the 50th person on the list. Then they call every 10,000th person after the 50th person.
4. The researchers call every person in each of 10 area codes that were randomly chosen.
5. The researchers number every American, and then call all randomly selected Americans.

9. A biologist is looking to see the effect of microgravity on plant growth. The researcher sends some seeds to the International Space Station, and has the height of the plants measured on specific days. The researcher also plants the same number of seeds in a laboratory on Earth, using the same lighting, soil, and water conditions, and measures the height of the plants on specific days. Describe the treatment group and the control group.
10. To see if a new blood pressure medication works or not, volunteers are divided into two groups. One group is given the new medication and the other group is given an older medication. Describe the treatment group and the control group.

11. In each situation state if a placebo is needed or not and explain your reasoning.

1. A new medication for treating heartworm in dogs is being investigated to see if it works.
2. A new training method for managers is being investigated to see if it improves morale.
3. A new medication is being tested to see if it reduces itching due to eczema.

12. In each situation state if a placebo is needed or not and explain your reasoning.

1. A new drug is being developed to treat high blood pressure and needs to be tested to see if it works better than a previous type of drug.
2. A new medication is being developed to treat headaches.
3. A new drink flavor is being developed to see if it is marketable.

13. To see if a new medication works to reduce fevers, volunteers are divided into two groups. One group is given the new medication, and the other group is given a placebo. The volunteers do not know which group they are in, but the researchers do. Is this a blind or double blind study?

14. To see if a new blood pressure medication works or not, volunteers are divided into two groups. One group is given the new medication and the other group is given the old medication. The volunteers do not know which group they are in, and neither do the researchers. Is this a blind or double blind study?

15. In each situation, identify a potential source of bias and explain your reasoning.

1. A study on teenage boys shows that a new drug works on curing acne. The company then concludes that the new drug will work on everyone.
2. A radio station asks listeners to phone in their choice in a daily poll.
3. The Beef Council releases a study stating that consuming red meat poses little cardiovascular risk.
4. A poll asks, “Do you support a new transportation tax, or would you prefer to see our public transportation system fall apart?”
5. A study is conducted on whether artificial light is better for plants. A certain type of plant is grown under artificial light and its height is recorded. A different type of plant is grown under natural light and its height is recorded. Both plant groups get the same amount of water and soil.

16. In each situation, identify a potential source of bias and explain your reasoning.

1. A study is conducted to see if grades improve if students are given tutoring. Students in a calculus class are given tutoring and compared to students in a statistics class who are not given tutoring.
2. An organic grower conducts a study and shows that pesticides are harmful to people who eat food that used the pesticide.
3. A poll asks, “If 53% of all people will need assisted living in the future, should you worry about needing assisted living insurance?”
4. A website asks people to say if they support the President or not.
5. A study of behavior modification therapy is tried on a specific breed of dogs. The study concludes that the behavior modification therapy works on all breeds of dogs.

17. The average SAT test scores for Michigan students in reading for the years 1971 to 2012 are given in the table below (College Board: Michigan, 2012). Create a table showing frequencies and relative frequencies for the data using the classes of 490 to 496, 497 to 503, 504 to 510, 511 to 517, 518 to 524, and 525 to 531.

496	500	502	504	505	507	509
497	500	503	504	505	507	512
499	500	503	505	505	508	521
499	500	504	505	506	508	523
499	501	504	505	507	509	530
500	502	504	505	507	509	509

18. The average hourly earnings of all employees in the U.S. in professional and business services for each month in the time period from March 1, 2006 to June 1, 2013 is given in the table below (Federal Reserve Bank of St. Louis, 2013). Create a table showing frequencies and relative frequencies for the data using the classes of 23 to 23.9, 24 to 24.9, 25 to 25.9, 26 to 26.9, 27 to 27.9, and 28 to 28.9.

23.40	23.81	24.85	25.72	26.73	26.84	27.19	27.23	27.74
23.87	24.22	24.44	25.46	26.74	26.98	27.14	27.39	27.48
23.23	24.42	24.91	25.47	26.89	26.98	27.43	28.19	27.67
23.14	24.56	24.65	25.72	27.37	26.88	26.96	27.81	28.09
23.68	24.45	24.80	25.59	27.32	27.27	27.06	27.55	27.79
23.31	24.84	25.33	25.66	27.02	27.19	27.31	27.57	27.97
23.64	24.46	25.33	25.89	26.84	27.32	27.18	27.84	28.55
23.97	24.45	25.48	26.05	26.74	27.49	27.21	27.45	28.17
28.03	28.30	27.85	27.76	28.24	27.68	28.27	27.90	28.04
28.58	28.56	28.61	28.43	28.38	28.24	28.57

19. Create histogram of the data in problem 17. State the overall shape of this histogram.

20. Create a relative frequency histogram of the data in problem 17. State the overall shape of this histogram.

21. Create histogram of the data in problem 18. State the overall shape of this histogram.

22. Create a relative frequency histogram of the data in problem 18. State the overall shape of this histogram.

23. In Kenya, the government is interested in the number of health care facilities in each of the provinces. Below is a table showing this data in 2013 (Kenya Open Data, 2013).

Province: * The province’s name was missing from the original data.	Number of facilities
RIFT VALLEY	1645
EASTERN	1093
NYANZA	962
NAIROBI	878
COAST	765
CENTRAL	745
WESTERN	541
N. EASTERN	131
*	9
PROV	3

1. Draw a bar graph of the data.
2. Draw a pie chart of the data.

24. According to the Pew Research Center, the percentage of people who own a particular smartphone is given in the table (Smith, 2011).

Platform	Percentage
Android	35%
iPhone	24%
Blackberry	24%
Palm device	6%
Windows phone	4%
Unspecified	7%

1. Draw a bar graph of the data.
2. Draw a pie chart of the data.

25. The following is a multiple line graph of unemployment percentages for the four corner states (Arizona, Colorado, New Mexico, and Utah). ("Unemployment Rate," n.d.) Compare and contrast the data for the four states, describing in detail at least three observations you identify from the graph.

26. Below are the temperatures in the United States on July 16, 2013 at 8 am EDT (National Weather Service, 2013).

Temperature of U.S. on July 16, 2013 at 8 am EDT.

1. What temperature range did Arizona have on that day?
2. What temperature range did Montana have on that day?
3. What temperature range did Texas have on that day?

27. The following graph is the salaries and unemployment rate for different levels of education. ("Employment Projections,” n.d.) Describe in detail at least three observations you identify from the graph.