Pew research on middle class

Part 1

1. Explain what is meant by the term a simple random sample, and then offer an example.

A simple random sample is simply a sample where all of the items in the sample pool have an equal chance of being chosen. For example, a sample size of 25 would lead to each item have exactly a four percent chance (100 / 25 = 4%) of being chosen.

2. Indicate the difference between a simple random sample and a stratified random sample.

In a simple random sample, the entire sample is one group. There is no subdivision. In a stratified random sample, the larger group is subdivided into smaller groups based on the shared traits that smaller parts of the sample have. For example, a sample where red and blue marbles are separated would be a stratified sample. If they are all left in one pool, that would be a simple sample.

3. Explain what is meant in sampling by the term sampling bias. Then, provide an example of sampling bias.

Sample bias is basically any situation where a sample is not truly random. If a sample pool is ostensibly a simple one but not all of the items in the sample have an equal chance of being chosen, then there is at least one form of bias present.

4. Identify some of the problems that arise when taking surveys.

There are a number of problems. Just a few of them would be getting a good sample of respondents (e.g. avoiding sample bias issues), designing the questions correctly, giving the right options for those questions and so forth so as to get a sample that is represented of the question asked. If the sample or the survey questions themselves (or both) are flawed, the results will be flawed as well.

5. Suppose that you must choose an SRS of 20 of the 450 retail outlets in New York that sell your company’s products. How would you label this population to select a simple random sample?

a) 001, 002, 003, …, 449, 450

b) 000, 001, 002, …, 449, 450

c) 1, 2, 3, …, 449, 450

B would not work in that it would have 451 items…not 450 (000 would be the extra). I would also not choose C because it would be better to have the same syntax/number of digits for all sample items. In other words, 001 should be used instead of 1.

6. A large retailer prepares its customers’ monthly credit card bills using an automatic machine that folds the bills, stuffs them into envelopes, and seals the envelopes for mailing. The retailer wants to determine if the envelopes are completely sealed. Inspectors choose 40 from the 1,000 stuffed each hour for a visual inspection.

a) What is the population for this sample survey?

b) What is the sample? 

The 40 envelopes selected for review are the sample. The 1000 envelopes from the whole group is the population.

Part 2

1. A telephone marketing company called 2000 randomly chosen residential telephone numbers and asked to talk to an adult member of the household. The interviewer asked, “What number of movies have you watched in a movie theater in the past year?”

a) What population does the telephone poll have in mind?

Adults who live in the overall geographic area from which the phone numbers are selected.

b) In all, 831 people responded. Give the rate of nonresponse for this survey.

A total of 1169 people did not response (2000 – 831 = 1169). 1169 is 58.45 percent of the whole (1169 / 2000).

c) What is the source of response error for the question asked? 

The primary issue would probably be the fact that most people will not precisely remember how many movies they saw over such a long time frame. Two weeks or a month would probably be a better time horizon.

2. The United States currently has approximately 287 Numbering Plan Areas (NPAs) in service, corresponding to geographic regions. Each NPA is identified by a three-digit code, commonly called an area code. Suppose that you want to choose an SRS of 15 of these area codes for a study of available telephone numbers. Label the codes 001 to 287 and use the Excel function RANDBETWEEN to a random sample. Hint, for information on the RANDBETWEEN function see the website, http://www.excel-easy.com/examples/random-numbers.html. 

Formula was =RANDBETWEEN(001,287)

3. The tickets issued by a movie theater are numbered serially. On August 6, 2016, the theater sold tickets with numbers beginning at 20860 and ending at 23102.