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HI6007 Statistics For Business Decisions

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Question:

Learning Outcomes:

  1. Students are able to apply appropriate business research methodologies to support decision-making process.

  2. Students are able to identify and apply valid statistical techniques in a given scenario to solve business problems.

  3. Students are able to justify and interpret the results of a statistical analysis in the context of critical reasoning for a business problem solving.

  4. Students are able to apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package.

  5. Students are able to justify and interpret statistical/analytical scenarios that best fit business solution.

  6. Students are able to justify value and limitations of the statistical techniques to business decision making.

Description:

Your task is to answer the following question

Question 1

In your own words, differentiate the following statistical terminologies with some examples.

a. Population Parameter and Sample Statistic

b. Descriptive Statistics and Inferential Statistics

c. Nominal Scale and Ordinal Scale

d. Primary Data Source and Secondary Data Source

Question 2

Data showing the population by state in millions of people follow (The World Almanac, 2012). The dataset in Excel file 2012Population.xlsx.

  1. Develop a frequency distribution, a percent frequency distribution, and a histogram.

 a

Use a class width of 2.5 million.

b.

Does there appear to be any skewness in the distribution? Explain.

c.

What observations can you make about the population of the 50 states?


Question 3

Forty-three percent of Americans use social media and other websites to voice their opinions about television programs (the Huffington Post, November 23, 2011). Below are the results of a survey of 1364 individuals who were asked if they use social media and other websites to voice their opinions about Television programs

 

Uses Social Media and Other Websites to

Doesn’t Use Social Media and

 

Voice Opinions About Television Programs

Other  Websites

to  Voice

 

 

Opinions   About

Television

 

 

Programs

 

Female

395

291

 

Male

323

355

 

 

a.

Show a joint probability table.

b.

What is the probability a respondent is female?

c.

What is the conditional probability a respondent uses social media and other websites to voice

 

opinions about television programs given the respondent is female?

d.

Let F denote the event that the respondent is female and A denote the event that the respondent uses social media and other websites to voice opinions about television programs.

 

Are events F and A independent?

 

Question 4

The average starting salary for this year's graduates at a large university (LU) is $20,000 with a standard deviation of $8,000. Furthermore, it is known that the starting salaries are normally distributed.

a. What is the probability that a randomly selected LU graduate will have a starting salary

of at least $30,400? 

b.

What is the probability that a randomly selected LU graduate will have a salary of exactly $30,400?

c.

Individuals with starting salaries of less than $15600 receive a low income tax break. What percentage of the graduates will receive the tax break?

d.

If 189 of the recent graduates have salaries of at least $32240, how many students graduated this year from this university?


Question 5

The College Board reported the following mean scores for the three parts of the SAT (The World Almanac, 2009):

Critical reading

502

Mathematics

515

Writing

494

 
Assume that the population standard deviation on each part of the test is 100.

a) What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical reading part of the test?

b) What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the  test? Compare this probability to the value computed in part (a).

 

Answers:

1.

  1. Population parameter refers to the population characteristics such as mean and standard deviation. The population mean is represented by µ while population standard deviation is indicated by the symbol sigma (Flick, 2015).

Sample statistic refers to the sample characteristics such as those describing the central tendency and the dispersion. For example, Xbar is used to indicate sample mean while s is used to denote sample standard deviation (Eriksson and Kovalainen, 2015).

  1. The statistical techniques which are deployed for summarising the sample data are collectively referred to as descriptive statistics. Typical examples of this would be sample statistics such as mean, median, standard deviation besides graphical techniques such as histogram and boxplot for the sample data (Hillier, 2016).

Inferential statistics captures those statistical techniques whose objective is to estimate the population parameters based on the sample data. Some of the popular inferential statistics techniques include hypothesis testing and confidence interval  (Eriksson and Kovalainen, 2015).

  1. Nominal scale refers to the measurement scale that is used to represent categorical data that lacks any natural order of arrangement. Typical examples would be colours, gender and race since the categorical data cannot be arranged in any order.

Ordinal scale refers to the measurement scale that is used to represent categorical data that have a natural order of arrangement. Typical examples would be the grading scheme of students using alphabets A to D.

  1. The primary data source is that data which has been directed collected using a survey or from the participants through various means which may include face to face interaction. On the contrary secondary data sources tend to indicate data which has been collected by someone else. For instance, census is a secondary data source comprising of information collected by different government agencies (Hair et. al., 2015).

2.

  1. The requisite distribution is shown below.

Histogram

  1. The above histogram has an asymmetric shape which is representative of skew. Further, from the histogram, it is evident that some states have exceptionally high population resulting in positive or right skew (Flick, 2015)..
  1. From the histogram, it is apparent that 90% of the states have a population that does not exceed 10 million. There are only two states out of 50 states i.e. 4% of the overall states which have a population in excess of 15 million. There is one state which has a population over 35 million.

3.

  1. Survey individuals = 1364 individuals

Computation table

Final Joint probability table

 

A

B

Total

Female

0.2896

0.2133

0.5029

Male

0.2368

0.2603

0.4971

Total

0.5264

0.4736

1

 

  1. Probability (Respondent = female)
  1. Conditional probability (Female respondent |Use Social Media)
  1. Whether being female(F) and Use Social Media (A) are independent events or not?

Event F &A aretermed as independent events when.

P (F∩ A) = P(F) * P(A)

In present case,

P (F∩ A) = (395/1364) = 0.289  

P(F) = (686/1364)

P(A) = (718/1364)

P(F) * P(A) = 0.265

The pre-requisite condition to classify as independent events are not satisfied which implies that being female (F) and Use Social Media (A) are not called as independent event.

4.

Average salary = $20,000

Standard deviation of salary = $8,000

  1. Probability (Salary >= $30,400)

 

  1. Probability (Salary exactly $30,400)

 

  1. % of graduate students receive tax break lower than $15600 =?

 

  1. Sample size of students = 189

Probability (Salary >= $32,240)

Assuming the number of graduatestudentsis N.

The equation can be formulated through N and probability and sample size.

0.0630 N = 189

N = 189/0.0630 = 3000

Number of graduate students is 3000.

5.

  1. Probability that sample mean test score within 10 points of population mean

Scores with 10 points of population mean of 502 are

 

  1. Probability that sample mean test score within 10 points of population mean

Scores with 10 points of population mean of 502 are

 

References

Eriksson, P. and Kovalainen, A. (2015) Quantitative methods in business research. 3rd ed. London: Sage Publications.

Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research project. 4th ed. New York: Sage Publications.

Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials of business research methods. 2nd ed. New York: Routledge.

Hillier, F. (2016) Introduction to Operations Research.6th ed.New York: McGraw Hill Publications.

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