1.2Sampling (Homework)

Explain the difference between a stratified sample and a cluster sample. (Select all that apply.)

In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included. In a stratified sample, random samples from each strata are included.

Explain the difference between a simple random sample and a systematic sample. (Select all that apply.)

In a simple random sample, every sample of size n has an equal chance of being included. In a systematic sample, the only samples possible are those including every kth item from the random starting position.

(b) Is it possible to include students sitting in row 3 with students sitting in row 2 in your sample?

No, it is not possible with this described method of selection.

Is your sample a simple random sample? Explain.

No, this is not a simple random sample. It is a cluster sample.

Marcie conducted a study of the cost of breakfast cereal. She recorded the costs of several boxes of cereal. However, she neglected to take into account the number of servings in each box. Someone told her not to worry because she just had some sampling error. Comment on that advice.

The advice is wrong. A sampling error only accounts for the difference in results based on the use of a sample rather than the entire population.

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.

Yes, your seating location and the randomized coin flip ensure equal chances of being selected.

(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) 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

An important part of employee compensation is a benefits package, which might include health insurance, life insurance, child care, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefits packages available in private businesses in Hawaii. You want a sample size of 100. Some sampling techniques are described below. Categorize each technique as simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample. (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

(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

(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

(c) Describe a process you could use to get a simple random sample of size 20 from a class of size 40.

Assign each student a number 1, 2, . . . , 40 and use a computer or a random-number table to select 20 students.