Statistics

In a statistical study what is the difference between an individual and a variable?

An individual is a member of the population of interest. A variable is an aspect of an individual subject or object being measured

(e) Instruct each MMH facility to survey 10 discharged patients this week and send in the results.

convenience sample

For a set population, does a parameter ever change?

never

Are data at the nominal level of measurement quantitative or qualitative?

qualitative

(a) An analysis of a sample of 31,000 patients from New York hospitals suggests that the poor and the elderly sue for malpractice at one-fifth the rate of wealthier patients. (Journal of the American Medical Association).

sampling

(a) Obtain a list of patients discharged from all MMH facilities. Divide the patients according to length of hospital stay (2 days or less, 3-7 days, 8-14 days, more than 14 days). Draw simple random samples from each group.

stratified sample

(d) At the beginning of the year, instruct each MMH facility to survey every 500th patient discharged.

systematic sample

(d) Use the Island Business Directory. Number all the businesses. Select a starting place at random, and then use every 50th business listed until you have 100 businesses.

systematic sample

(b) Consider these number assignments for category items describing usefulness of customer service. 1 = not helpful; 2 = somewhat helpful; 3 = very helpful; 4 = extremely helpful Are these numerical assignments at the ordinal data level? Explain.

Yes, the data has an ordering to its categories.

(a) Assign each business in the Island Business Directory a number, and then use a random-number table to select the businesses to be included in the sample.

simple random sample

(d) An Australian study included 588 men and women who already had some precancerous skin lesions. Half got skin cream containing a sunscreen with a sun protection factor of 17; half got an inactive cream. After 7 months, those using the sunscreen with the sun protection had fewer precancerous skin lesions (New England Journal of Medicine).

experiment

(b) Obtain lists of patients discharged from all MMH facilities. Number these patients, and then use a random-number table to obtain the sample.

simple random sample

(b) The effects of wind shear on airplanes during both landing and takeoff were studied by using complex computer programs that mimic actual flight.

simulation

(e) Group the businesses according to type: medical, shipping, retail, manufacturing, financial, construction, restaurant, hotel, tourism, other. Then select a random sample of 10 businesses from each business type.

stratified sample

What is the average miles per gallon (mpg) for all new hybrid small cars? Using Consumer Reports, a random sample of such vehicles gave an average of 35.7 mpg. 1) Identify the variable. 2) Is the variable quantitative or qualitative? 3) What is the implied population?

1) miles per gallon 2) quantitative 3) all new hybrid small cars

Government agencies carefully monitor water quality and its effect on wetlands (Reference: Environmental Protection Agency Wetland Report EPA 832-R-93-005). Of particular concern is the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill fish and wildlife. Twenty-eight samples of water were taken at random from a lake. The nitrogen concentration (milligrams of nitrogen per liter of water) was determined for each sample. 1) Identify the variable. 2) Is the variable quantitative or qualitative? 3) What is the implied population?

1) nitrogen concentration 2) quantitative 3) the entire lake

Categorize these measurements associated with a robotics company according to level: nominal, ordinal, interval, or ratio. 1) Salesperson's performance: below average, average, above average. 2) Price of company's stock 3) Names of new products 4) Temperature (°F) in CEO's private office 5) Gross income for each of the past 5 years 6) Color of product packaging

1) ordinal 2) ratio 3) nominal 4) interval 5) ratio 6) nominal

What is the difference between a parameter and a statistic?

A parameter is a numerical measurement describing data from a population. A statistic is a numerical measurement describing data from a sample.

If there are three different samples of the same size from a set population, is it possible to get three different values for the same statistic?

Data from samples may vary from sample to sample, and so corresponding sample statistics may vary from sample to sample.

(a) Consider these number assignments for category items describing electronic ways of expressing personal opinions. 1 = Twitter; 2 = e-mail; 3 = text message; 4 = Facebook; 5 = blog Are these numerical assignments at the ordinal data level or higher? Explain.

No, they are at the nominal level as there is no apparent ordering in the responses.

What about at the interval level or higher? Explain.

No, while the data has an ordering, and the data can be compared to each other, the differences don't mean anything.

Explain the difference between a simple random sample and a systematic sample.

Simple Random sample: every sample of size n has an equal chance of being included. Systematic sample: the only samples possible are those including every kth item from the random starting position.

Explain the difference between a stratified sample and a cluster sample.

Stratified sample: random samples from each strata are included Cluster sample: the clusters to be included are selected at random and then all members of each selected cluster are included.

(b) The Colorado Division of Wildlife caught 41 bighorn sheep on Mt. Evans and gave each one an injection to prevent heartworm. A year later, 38 of these sheep did not have heartworm, while the other three did.

This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured.

(c) The Colorado Division of Wildlife imposed special fishing regulations on the Deckers section of the South Platte River. All trout under 15 inches had to be released. A study of trout before and after the regulation went into effect showed that the average length of a trout increased by 4.2 inches after the new regulation.

This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured.

(a) The Colorado Division of Wildlife netted and released 774 fish at Quincy Reservoir. There were 219 perch, 315 blue gill, 83 pike, and 157 rainbow trout.

This is an observational study because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured.

(d) An ecology class used binoculars to watch 23 turtles at Lowell Ponds. It was found that 18 were box turtles and 5 were snapping turtles.

This is an observational study because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured.

In each of the following situations, the sampling frame does not match the population, resulting in undercoverage. Give examples of population members that might have been omitted. (a) The population consists of all 250 students in your large statistics class. You plan to obtain a simple random sample of 30 students by using the sampling frame of students present next Monday. (b) The population consists of all 15-year-olds living in the attendance district of a local high school. You plan to obtain a simple random sample of 200 such residents by using the student roster of the high school as the sampling frame.

a) Students who are skipping class cannot be sampled; Students who are on a school trip cannot be sampled; Students who are out sick cannot be sampled. b) Home-schooled students cannot be sampled and Dropouts cannot be sampled.

Consider the students in your statistics class as the population and suppose they are seated in four rows of 10 students each. To select a sample, toss a coin. If it comes up heads, you use the 20 students sitting in the first two rows as your sample. If it comes up tails, you use the 20 students sitting in the last two rows as your sample. (a) Does every student have an equal chance of being selected for the sample? Explain. (b) Is it possible to include students sitting in row 3 with students sitting in row 2 in your sample? Is your sample a simple random sample? Explain. (c) Describe a process you could use to get a simple random sample of size 20 from a class of size 40.

a) Yes, your seating location and the randomized coin flip ensure equal chances of being selected. b) No, it is not possible with this described method of selection; No, this is not a simple random sample. It is a cluster sample. c) Assign each student a number 1, 2, . . . , 40 and use a computer or a random-number table to select 20 students.

(c) A study of all league football scores attained through touchdowns and field goals was conducted by the National Football League to determine whether field goals account for more scoring events than touchdowns (USA Today).

census

(b) Use postal ZIP Codes to divide the state into regions. Pick a random sample of 10 ZIP Code areas and then include all the businesses in each selected ZIP Code area.

cluster sample

(c) Randomly select some MMH facilities from each of five geographic regions, and then include all the patients on the discharge lists of the selected hospitals.

cluster sample

(c) Send a team of five research assistants to Bishop Street in downtown Honolulu. Let each assistant select a block or building and interview an employee from each business found. Each researcher can have the rest of the day off after getting responses from 20 different businesses.

convenience sample