Question

exercises 1 - 3
name five ways that data can be collected.
what is meant by sampling error and nonsampling error?
why are random numbers used in sampling, and how are random numbers generated?
name and define the four basic sampling methods.
for exercises 5 - 10, define a population that may have been used and explain how the sample might have been selected.

1. time magazine reported that 83% of people with household earnings over $200,000 have a bachelor’s degree.
2. time magazine reported that 25% of the world’s prisoners and prisons are in the united states.
3. a researcher found that the average size of a household in the united states was 2.54 people.
4. adults aged 19 - 50 need 1000 milligrams of calcium per day. (source: institute of medicine report)
5. taking statins raises the risk of developing diabetes. (source: journal of american medical association and other sources)
6. the average january 2012 temperature in boston was 34.2°f. this was 5.2° higher than the normal january average temperature. (source: accuweather.com)

for exercises 11 - 16, identify the sampling method that was used.

1. to check the accuracy of a machine filling coffee cups, every fifth cup is selected, and the number of ounces of coffee is measured.
2. to determine how long people exercise, a researcher interviews 5 people selected from a yoga class, 5 people selected from a weight - lifting class, 5 people selected from an aerobics class, and 5 people from swimming classes.
3. in a large school district, a researcher numbers all the full - time teachers and then randomly selects 30 teachers to be interviewed.
4. in a medical research study, a researcher selects a hospital and interviews all the patients that day.
5. for 15 minutes, all customers entering a selected wal - mart store on a specific day are asked how many miles from the store they live.
6. ten counties in pennsylvania are randomly selected to determine the average county real estate tax that the residents pay.

Explanation:

1. Five ways to collect data: Surveys, experiments, observations, interviews, and secondary - data analysis. Sampling error is the difference between sample and population values due to chance in sampling. Nonsampling error includes all errors not due to sampling like data - entry errors. Random numbers ensure unbiased sampling and can be generated by software, random - number tables etc. The four basic sampling methods are simple random (every member has equal chance), stratified (divide population into strata and sample from each), systematic (select every kth member), and cluster (divide into clusters and sample clusters).
2. For exercise 5, population could be all people with household earnings over $200,000. Sample might be obtained through surveys of such households. For exercise 11, it's systematic sampling as every fifth cup is selected. For exercise 12, it's stratified sampling as different exercise - class strata are sampled. For exercise 13, it's simple random sampling as teachers are randomly selected. For exercise 14, it's cluster sampling as a hospital (a cluster) is selected and all patients are interviewed. For exercise 15, it's convenience sampling as customers entering a specific store are sampled. For exercise 16, it's cluster sampling as counties (clusters) are sampled.

Answer:

1. Five ways to collect data: Surveys, experiments, observations, interviews, secondary - data analysis. Sampling error: Difference due to chance in sampling. Nonsampling error: Non - sampling related errors. Random numbers for unbiased sampling, generated by software/tables. Four basic sampling methods: Simple random, stratified, systematic, cluster.
2. Exercise 5: Population - All people with household earnings over $200,000. Sample - Through surveys of such households.

Exercise 11: Systematic sampling.
Exercise 12: Stratified sampling.
Exercise 13: Simple random sampling.
Exercise 14: Cluster sampling.
Exercise 15: Convenience sampling.
Exercise 16: Cluster sampling.