Reference no: EM132294533
Quantitative Analysis Assignment -
Learning Outcomes -
a) Examine the statistical techniques for the quantitative evaluation of data in decision making for business applications.
b) Identify and apply appropriate statistical techniques to the problems and challenges.
c) Students will develop analytical and statistical skills through Excel data analysis to manipulate data into meaningful information for the purpose of decision making.
Context: The main aims to develop students' competency in statistical literacy for decision making in the local and global business environment. It reviews statistical techniques for the quantitative evaluation of data in Financial applications. Students will develop analytical and statistical skills to enable them to transform data into meaningful information for the purpose of decision making.
Objectives:
- To more broadly understand the statistical literacy for decision making.
- Interpret statistical results and communicate their statistical analysis in business reports.
Instructions: This assignment requires you to apply statistical knowledge and skills.
- You will specify a descriptive summary statistics, for this assignment. This model can be based on a theory, several theories, your experience, and/or ideas.
- Please use Excel for statistical analysis in this assignment. Relevant Excel statistical output must be properly analysed and interpreted.
- Please provide a number for every table, graph or figure used and make clear reference to the table/graph/figure in your discussion.
- The word limit for this group assignment is 2,000 words (excluding Excel output).
Assignment tasks -
The dataset included with this assignment is a random sample of 400 persons from the population survey of a US state (say, California) in a certain year (say, 2012). The population consists of individuals in the said US state who were working and drawing wages during the survey year, which you can access from the Assessment Information page on the unit website.
You need to select the random samples of 50 IDs each containing observations, where appropriate, of the four variables V1 to V3. The variables for this assignment are as follows:
V1) Wage (dollars per hour)
V2) Occupational category (1=Management, 2=Sales, 3=Clerical, 4=Service, 5=Professional, 6=Other)
V3) Indicator variable for sex (1=Female, 0=Male).
Task 1: Selecting your Random Sample and Creating your Sample Data File
In order to select the sample data that will form the basis of your assignment you will need to make use of the random number table provided with this assignment. The provided table of random numbers is, as the title suggests, a sequence of randomly generated numerical digits (0 to 9). These digits are arranged in a table with one hundred rows numbered 01 to 00 and twenty columns spread over two pages. The entries in each column of each row consist of five single digits.
The wages data from which you will select your sample data consists of 400 IDs each with an identifying person number (PN) ranging from 1 (or 001) to 400.
Your first task is to select 50 three digit random (wages) numbers ranging from 001 to 400 from the provided table of random numbers. We will ask you to select 50 numbers, to begin with, just to cover the distinct possibility that you may select the same three digit number more than once. The type of simple random sampling that we will be engaged in here is termed "without replacement" because we specifically do not want to allow a personal identification number to be selected more than once.
In order to select your 50 random personal identification numbers you will need to first go to a starting position row and column in the random number table. Defined by the last three digits of your Torrens University student identification number. The last two digits of your Torrens ID number identifies the row and the third last digit identifies the column of your (relatively) "unique" starting position.
For the demonstration last three digits of 312, reading across row 12 from left to right starting at column 3 as instructed, you would encounter the following three digit numbers;
293 313 381 349 295
You need to record these first three acceptable ID numbers, 293, 313, 381 and 349 into the first column of an Excel spread-sheet and then continue this process until fifty valid three-digit personal identification numbers selected.
(a) Use excel to draw the column chart and pie chart for Indicator variable for sex (1=Female, 0=Male).
Task 2: Probability distribution and Binomial distribution
(a) Find the frequency distribution for the Occupational category (1=Management, 2=Sales, 3=Clerical, 4=Service, 5=Professional, 6=Other). Use Excel to produce a Descriptive Statistics table for your sample "Occupational category" data and paste into your MS Word assignment document.
(b) Use the relative frequency approach to find the probability distribution for the Occupational category.
(c) Draw the bar chart for the probability distribution of Occupational category.
(d) Define the probability distribution based on part (b), for example (You have to calculate according to your data from task 1)
|
x
|
1
|
2
|
3
|
4
|
5
|
6
|
|
P(x)
|
0.14
|
0.26
|
0.3
|
0.15
|
0.08
|
0.07
|
(e) Based on the probability distribution calculate the following
i. Find the probability of exactly two.
ii. Find the probability more than two.
iii. Find the probability at least three.
(f) According to a report of the sample data based on your sample information, for example in this case 26% (you need to consider the sales proportion as the probability of success) of the Occupational category. Assume that a sample of n=10 people is studied.
i. Find the probability of exactly two.
ii. Find the probability less than two.
iii. Find the probability at least six.
Task 3: Estimation and Hypothesis Testing
(a) Use Excel to draw histogram for your sample "Wages (dollar per hours)" data.
(b) Use Excel and your sample data file to produce a suitable output, to test, at the 1% level of significance, the hypothesis that, for Wages (dollar per hours) in the population with mean is 25 $.
(c) Is this a one-tailed or two-tailed test? Briefly explain the reasoning behind your answer.
(d) Write, in precise symbolic form, the null and alternative hypotheses.
(e) Define Z or T test and also calculate the value of test statistics.
(f) Define critical values based on the nature of the problem.
(g) State the conclusion based on the sample evidence.
(h) Find 99% confidence interval for the Wages (dollar per hours) in the population.
(i) Reconsider this procedure at the 5% level of significance, the hypothesis that, for Wages (dollar per hours) in the population with mean is greater than 25 $.
(j) Make the decision based on the critical value.
(k) Find 95% confidence interval for the Wages (dollar per hours) in the population.
(l) Find precision and also interpret the confidence interval.