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Content: Charles A. Dana Center at The University of Texas at Austin © SECTION 3-1 Modified Student Worksheets: Matthew M. Winking at Phoenix High School

Sec 3.1 – Statistical Studies

Definitions Name: 1. POPULATION:

Parameter [Greek variables] :

2. SAMPLE:

Statistic [English variables] :

3. List reasons why you might use a SAMPLE study instead of a POPULATION study?

4. A recent survey by the alumni of a major university indicated that the average salary of 8,500 of its 250,000 graduates was $123,000. Does this value describe a parameter or a statistic? WHY?

5. A survey of 976 American households found that 32% of the households own two cars. Identify the

population and the sample. SAMPLE: POULATION:

For # 6– 8 Identify each of the following data sets as either: (P) Population or (S) Sample

_______6. ….the age of a few randomly selected participants in a study about a race of runners

_______7. ….the annual salary of each full-time teacher in a study about Phoenix High School

_______8. ….a survey of 750 Georgia homeowners in a study about all of Georgia’s homeowners.

For # 9 – 11 Identify each of the following numerical values as either: (P) Parameter or (S) Statistic

_______9. …. of a company’s employees the opinion of just those that were there on time one morning about

what they thought of a new training program.

_______10. …. in a study about a small company of 25 employees, the range of their employee’s salaries

_______11. …. in a study about the value of American homes in 2012, the average decrease of all the homes sold

in Gwinnett.

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TYPES OF SAMPLES

12. Simple Random sample:

13. Stratified sample:

14. Cluster sample:

15. Systematic sample:

16. Convenience sample:

Choose which sampling technique is used.

(R) Random (STR) Stratified (CLS) Cluster (CON) Convenience (SYS) Systematic

_______ 17. There are 250 seventh graders and 300 eighth graders at Generic Middle School. We ask 45

seventh graders and 50 eighth graders how many siblings they have to compare the two groups.

_______ 18. I ask all freshmen, no sophomores, no juniors, and all seniors if they prefer Vanilla or Cherry Coke

(these four groups are my only four groups) to create a study of what should be in the vending

machines.

_______ 19. I ask everyone in my 5th

period class who has more than one computer at home in a study about all

of my students for the year.

_______ 20. I collect data from every 15th

student on my list of the entire school population.

_______ 21. After using a random number table to generate two-digit numbers, I decide on 10 people to choose

from the population.

Rank the sampling types in order from what would usually be the WORST to BEST representation of a

POPULATION. Provide brief explanations (especially if the ranking depends on the study).

(R) Random (STR) Stratified (CLS) Cluster (CON) Convenience (SYS) Systematic

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Types of Studies Name: TYPES of STUDIES and DATA COLLECTION METHODS

1. Observational Study:

2. Experimental Study:

Treatment Group:

Control Group & Placebo: 3. Simulations:

4. Census:

5. Sampling:

Choose the type of Study that is most likely to be used (each is used just once). (E) Experimental (SIM) Simulation (C) Census (SMP) Sampling (O) Observational

________ 6. You want to know how many pets the teachers at Phoenix High School own.

________ 7. A drug is given to 15 patients and a placebo to another group to determine its effect on an illness. ________ 8. You are doing a study at a mall in which you are counting the number of men that wash their

hands after using the restroom. ________ 9. You want to know the g-forces a person would experience during a fall from a 90 foot high bridge

into a lake. ________ 10. You need data on the average number of hours worked per week by an American teenager with

a part-time job.

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Experimental Study A 17-year-old student designed a science fair project with 72 mice randomly assigned to three groups: hard rock music, Mozart, and no music at all (called a control group). The mice in the first two groups were exposed to music 10 hours a day. Three times a week, all of the groups were timed as they ran through a maze. An analysis of results showed that the 24 mice in the no-music group averaged about a 5-minute improvement in their maze completion time, while the Mozart mice improved 8.5 minutes. The hard rock mice actually got slower—an average of four times slower! Another interesting fact: The student had to start his experiment over because all the hard-rock mice killed each other. None of the classical mice did that.

(Wertz, M. [1998]. Why classical music is key to education. From www.schillerinstitute.org/programs/program_symp_2_7_98_tchor_.html#Music_Mice_Mazes)

11. Describe the independent variable (sometimes referred to as the treatment variable).

12. Describe the dependent variable (sometimes referred to as the variable of interest).

13. Which group(s) would be considered the treatment group?

14. Which group(s) would be considered the control group?

A researcher wanted to study the effects of the amount of time of physical exercise and academic grade point average for a statistics class. The researcher found that the students that exercised also slept more as a result of their exhaustion from exercise and therefore couldn’t only attribute the increase in the grade point average to physical exercise.

15. Describe the independent variable (sometimes referred to as the treatment variable).

16. Describe the dependent variable (sometimes referred to as the variable of interest).

17. A confounding variable is sometimes an unexpected variable that can adversely affect the relation between the designed independent and dependent variables which may cause the researcher to analyze the results incorrectly. What is the confounding variable in this study?

18. Describe how the researcher might instead conduct an observational study about the effect of exercise and physical exercise.

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Additional Experimental Study Types:

Blind Study:

Double Blind Study: Placebo Effect:

A researcher wanted to study the effects of a motion sickness medicine. The primary researcher had a third independent party create 25 containers containing a placebo and 25 containers containing the actual medicine. The containers were all numbered. The researcher then gave a medicine to 50 patients that suffer from motion sickness on a cruise ship. The researcher nor the participants knew which participants received the placebo and which received the actual treatment. The researcher conducted the study and only after the initial study was completed did the third party reveal which numbered containers were the placebo and which were not.

19. What type of experimental study was used in this study?

A researcher wanted to study the effects of a new migraine headache medicine at a neurologist’s clinic. The researcher found 50 patients agreed to participate in the clinical trials. The researcher gave the first 25 patients the real treatment medicine and labeled those participants treatment group ‘A’. The researcher gave a placebo to the next 25 patients a placebo that looked like and tasted like the real medicine. These participants were labeled the control group ‘B’.

20. What type of experimental study was used in this study?

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Null and Alternative Hypothesis Name: Consider this situation: “This unopened bag of chips is half empty. I wonder if it really contains 28.3 grams as the package says?” This type of informal question or observation is the beginning of many investigations. “Do Spud Potato Chips contain an average of 28.3 grams of chips per bag?”

1. Suppose you conduct the investigation into Spud Potato Chips and find that the mean weight of the chips

in your sample is 25 grams, rather than 28.3 grams ( x = 25 grams). Do you think that a difference of 3.3 grams between the actual and advertised weights is large enough that it needs to be reported? If so, how do you report this information and to whom?

In some situations, researchers are even more formal and state hypotheses. In a case like this, the null hypothesis (Ho) generally states that there is no difference between the true value and the claimed value. The alternative hypothesis (Ha) states that something is different, incorrect, or that something has changed.

2. What are the null and alternative hypotheses for the potato chip example?

Ho: The true mean weight . Ha: The true mean weight .

To be concise, researchers often use symbols in place of words. Greek letters are usually used when referring to populations (the entire group being studied, from which a sample or samples will be drawn). English letters are used for samples (the particular items or individuals included in a particular study). For example, when discussing the mean:

μ = the population mean (Greek letter mu—pronounced mew) = the sample mean (pronounced x-bar)

3. So the hypotheses for a study can be stated in words or symbols. When using symbols, you must identify

what your symbols represent. Use the symbol μ and inequality symbols to restate the hypotheses in #2.

Ho: Ha:

4. What would you do next to determine which of these hypotheses is true?

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For Questions 5 through 9, practice writing hypotheses. Write them in words and then convert them to symbols. Finally, sketch or outline a simple study design that might help study the hypotheses.

5. A local pizza shop advertises “an average delivery time of 20 minutes or less,” but it

does not offer a guarantee such as a free pizza. The national manager, Su Lin, wonders if her employees are fulfilling the claim.

6. James believes that his mother’s houseplants would grow taller if she watered with rainwater instead of tap water.

7. According to the 2005 U.S. Census Bureau, at least 10.2% of registered births in the United States in 2005 were to teenage mothers. A sociologist believes that this percentage has increased since then.

8. According to the Federal Housing Finance Board, the mean price of a single-family home in 2005 was $299,800. A real estate broker believes that because of recent down turn in home sales that the mean price has decreased since then.

9. Justin flipped a spun a penny from 1985 eight times and got the results T, T, T, T, T, T, T, T. He believes the penny might be defective and the probability of landing on Tails this way is greater than 50%. (Try experimenting with this. You might be surprised what happens with all pennies 1985 and before)

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Margins of Error Name: According to a recent study in 2014 by the RAND corporation, in the U.S. 9.3 million more people have gained health care coverage over the previous year with an error of ±3.5 million people based on the statistical study.

1. This type of error in a study is often referred to as a margin of error. a. What is the least number of people that have gained coverage based on the study?

b. What is the most number of people that have gained coverage based on the study?

2. A recent study in 2013 conducted in Canada showed that house values were reduced in value by an average amount of 15% with a margin of error of ±4.9% because the previous owner smoked in the house.

a. What is the maximum percentage the house value average could have been reduced?

b. The median house price in a Ontario Canada was equivalent to $244,000 US dollars. What might be the worst possible average price for home owners that have smokers in their house (i.e. use the maximum possible reduced value percentage from part “a”)?

3. A study conducted at a school showed that the batteries used by calculators lasted an average of 101 days with a margin of error of ±9 %.

a. What is the minimum average number of days a teacher can expect to have the batteries last in her classroom?

b. There are roughly 279 days from the first day of school until the last day of school, The teacher has 24 TI-84 calculators and each one requires 4 triple A batteries. If the teacher can buy triple A batteries whole sale at 52 cents a battery, how much do you think she will need to spend at most on batteries for calculators over the year?

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4. According to a recent 2013 government study, the average 4-year education at a public college or university will cost about $8,944 per year with a margin of error of ±7.2 %.

a. What is the minimum average cost of tuition?

b. What is the minimum average cost of tuition?

c. Living Expenses and books are expected to cost another $11,120 per year with a margin of

error of ±5.2 %. What is the maximum average cost for the additional expenses?

d. If the college you plan to attend charges that are roughly the average amount, what is the maximum amount you will need to spend for a 4-year bachelor’s degree including tuition, living expenses, and books (and assuming you attend for 4 years).

5. A new anti-viral flu study found that participants that took their medication found the flu lasted an average of 2.8 days with a margin of error of ± 11.3%. A control group that did not take any anti-viral medicine found that the flu lasted 4.1 days with a margin of error of ± 15.3%.

Could you guarantee that average of those taking the new anti-viral medicine had an average of less time having the flu? Explain.

6. Confidence intervals are commonly created that bound a population parameter with a certain level of confidence. Using a very high confidence interval, the median salary for a Georgia Household in 2013 was determined by a government census to be between $45,400 and $53,800.

a. In a newspaper they wanted to use a point estimate (i.e. a single number) to represent the median salary. What should be the point estimate based on the interval?

b. The newspaper also wanted to list the margin of error. List the margin of error as both a dollar amount and as a percentage of the point estimate.

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