Assignment Task: Tutorial Questions
Purpose: This assignment is designed to assess your level of knowledge of the key topics covered in this unit.
Unit Learning Outcomes Assessed:
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 a selection of tutorial questions for weeks 2 to 6 inclusive and submit these answers in a single document. The questions to be answered are;
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.
a. Develop a frequency distribution, a percent frequency distribution, and a histogram. 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 Voice Opinions About Television Programs
Doesn't Use Social Media and Other Websites to Voice Opinions About Television Programs
|
|
Uses Social Media and Other Websites to Voice Opinions About Television Programs
|
Doesn't Use Social Media and 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).
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