Problem 1

Problem Cola wars is the popular term for the intense competition between Coca-Cola and Pepsi displayed in their marketing campaigns. Their campaigns have featured claims of consumer preference based on taste tests. Recently, the Huffington Post (Nov. 11, 2013) conducted a blind taste test of 9 cola brands that included Coca-Cola and Pepsi. (Pepsi finished 1st and Coke finished 5th.) Suppose, as part of a Pepsi marketing campaign, 1,000 cola consumers are given a blind taste test (i.e., a taste test in which the two brand names are disguised). Each consumer is asked to state a preference for brand A or brand B.

a. Describe the population. Cola consumer

 b. Describe the variable of interest. Cola preference

c. Describe the sample. 1000 cola consumer

d. Describe the inference. The generalization of the Cola preference

 

Problem 2.

Refer to Problem 2, in which the cola preferences of 1,000 consumers were indicated in a taste test. Describe how the reliability of an inference concerning the preferences of all cola consumers in the Pepsi bottler’s marketing region could be measured.

From this particular scenario, it implies that preferences of 1,000 consumers have been used in a particular region. It hence implies that the preferences of the total population will not be mirrored in such estimate. An example can be used to illustrate such scenario. Given that 60% of the 1.000 Coca Cola consumers prefer the Pepsi brand, it is not an indicator that the same percentage of the participants prefer Pepsi. Also, the statistical reasoning can still be applied in this particular scenario. That is, if the estimate of the preference towards Pepsi is within the limit of 6%, it will imply that the preference will be between 54% (60-6) and 66% (60+6). The interval therefore is a measure of the reliability of the inference.

3. Answer the following questions

1. What is statistics?

Statistics is the science  of data. It involves collecting,  classifying,  summarizing, organizing, analyzing, and interpreting numerical information.

2. Explain the difference between descriptive and inferential statistics.

-Involves: collecting  data? presenting  data? characterizing  data

- Purpose: describe  data

3. List and define the four elements of a descriptive statistics problem.

1. The population  or sample  of interest

2. One or more variables  (characteristics  of the population  or sample  units) that are to be investigated

 3. Tables,  graphs,  or numerical  summary  tools

4. Identification  of patterns  in the data

4. List and define the five elements of an inferential statistical analysis.

1. The population  of interest

2. One or more variables  (characteristics  of the population  units) that are to be investigated

3. The sample  of population  units

4. The inference  about the population  based  on information  contained  in the sample

5. A measure  of reliability  for the inference

5. List the three major methods of collecting data and explain their differences.

 

(Obtaining Data)

-Published source: book, journal, newspaper, Web site

-Designed experiment:researcher  exerts strict control over units

-Survey:a group of people are surveyed  and their responses are recorded

-Observation study: units are observed in natural setting and variables of interest are recorded

 

(Samples)

 A representative sample exhibits characteristics typical of those possessed by the population of interest.

A random sample of n experimental  units is a sample selected  from the population in such a way that every  different  sample of size n has an equal chance  of selection.

(Random Sample)

Every  sample of size n has an equal chance  of selection.

6. Explain the difference between quantitative and qualitative data.

Quantitative Data :measured on a numeric scale.

Qualitative Data: classified into categories.

7. Explain how populations and variables differ.

A population is a set of units that we are interested in studying, while a variable refers to characteristics or property of an individual experimental unit in the population

8. Explain how populations and samples differ.

 A population is the entire group that you want to draw conclusions about.

A sample is the specific group that you will collect data from. The size of the sample is always less than the total size of the population.

9. What is a representative sample? What is its value? 

A representative sample is a small number of people that reflect, as accurately as possible, a larger group. Then we can apply, for example, an online survey to a sample of the population looking for it to be the most representative of our target population.

Representative samples are important as they ensure that all relevant types of people are included in your sample and that the right mix of people are interviewed. If your sample isn't representative it will be subject to bias. The reason for the inaccuracy of the poll was an unbalanced, unrepresentative sample.