Mathematics And Statistics

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Assessment Details
 
Mathematics and Statistics
 
 
 
Assessment Tasks
 
Answers to the Assessment 3 tasks must be based on the sample data file that you created in Part I of the assignment. Most tasks in the assessment task 3 require you to obtain an Excel output prior to performing some analysis. There are five tasks in the Assessment 3. You must meet all task requirements to receive full marks.
 
Task 1 (20 marks)
 

  1. 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.

 

  1. Use the relative frequency approach to find the probability distribution for the Occupational category.

 

  1. Draw the bar chart for the probability distribution of Occupational category.

 

  1. Define the probability distribution based on part (b), for example (You have to calculate according to your data)

 

x 1 2 3 4 5 6
P(x) 0.14 0.26   0.3   0.15   0.08   0.07

 

  1. Based on the probability distribution calculate the following

 

  1. Find the probability of exactly two

 

  1. Find the probability more than two

 

  • Find the probability at least three

 
Task 2 (20 marks)
 

  1. Find the frequency distribution for the Indicator variable for union membership (1=Union member, 0=Not union member). Use Excel to produce a Descriptive Statistics table for your sample “union membership” data and paste into your MS Word assignment document.
  2. Use the relative frequency approach to find the probability distribution for the union membership.

 

  1. Draw the bar chart for the probability distribution of union membership.

 

  1. Define the probability distribution based on part (b), for example (You have to calculate according to your data)

 

x 0 1
P(x) 0.54 0.46

 

  1. Based on the probability distribution draw the bar chart.

 

  1. According to a report of the sample data, 46% (you need to consider the union member proportion as the probability of success) of the people have the union membership. Assume that a sample of 8 people is studied

 
 
 

  1. Find the probability of exactly two

 

  1. Find the probability less than two

 

  • Find the probability at least six

 
Task 3 (20 marks)
 

  1. 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 $27.
  2. Is this a one-tailed or two-tailed test? Briefly explain the reasoning behind your answer.

 

  1. (c) Write, in precise symbolic form, the null and alternative hypotheses.

 

  1. Define Z or T test and also calculate the value of test statistics.

 

  1. Define critical values based on the nature of the problem.

 

  1. State the conclusion based on the sample evidence.

 

  1. Find 99% confidence interval for the Wages (dollar per hours) in the population.

 

  1. 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 $27.

 

  1. Make the decision based on the critical value.

 

  1. Find 95% confidence interval for the Wages (dollar per hours) in the population.

 
 
Task 4 (20 marks)
 

  1. Use Excel and your sample data file to produce a descriptive summary output (remember to include confidence bound “e” at 5% level of significance), for Indicator variable for sex (1=Female, 0=Male) according to your sample data from task 1.
  2. Define the mean proportion.

 

  1. At 5% level of significance, the hypothesis that, for Indicator variable for sex (1=Female, 0=Male) according to your sample data from task 1 and the mean proportion for female population is 0.45.
  2. Write, in precise symbolic form, the null and alternative hypotheses.

 

  1. Is this a one-tailed or two-tailed test? Briefly explain the reasoning behind your answer.

 

  1. State the conclusion based on the sample evidence.

 

  1. Find 95% confidence interval for the Indicator variable for sex female.

 
 
Task 5 (20 marks)
 

  1. Find the relationship between Wages (dollar per hours) as a response variable and number of years of work experience as an explanatory variable. Use excels to find the linear regression output. The belief is that as the work experience increases the wages (dollar per hours) would increase. (You have to calculate according to your data).

 

  1. State the slope coefficient of the least square regression equation.

 

  1. State the intercept coefficient of the least square regression equation.

 

  1. Determine the least square regression equation representing the approximate linear relationship between the Wages (dollar per hours) as a response variable and Number of years of work experience as an explanatory variable.

 

  1. Estimate the Wages when the work experience is 25 years.

 

  1. Construct the 95% confidence interval for the slope parameter of the least square regression equation.

 
 
 
 
 
Marking Information: The case study assessment will be marked out of 100 and will be weighted 30% of the total unit marks.
 

Marking Criteria Not satisfactory Satisfactory   Good   Very Good Excellent
  (0-49%) of the (50-64%) of the   (65-74%) of the   (75-84%) of the (85-100%) of the
  criterion mark) criterion mark   criterion mark   criterion mark criterion mark
               
Theoretical All the tasks are not Some questions are   Majority of the   Majority of the All questions are
understanding of interpreted, and correctly answered   questions are   questions are correctly answered,
statistical data questions are not but most questions   correctly answered   correctly answered, and significance of the
analysis (20 marks) correctly answered. are partially correct.   but significance of the   and significance of the result is well
        result is not explained   result is explained explained to show its
              practical relevance.
Problem set-up in Fail to set-up problem Statistical data   Statistical data   Statistical data Statistical data
Excel (30 marks) correctly in excel. analysis is correctly   analysis is correctly   analysis is correctly analysis is correctly
    set-up, but all other   set-up in excel with   set-up in excel with set-up in excel with all
    relevant information   most of the of correct   majority of correct & correct & relevant
    pertaining to analysis   & relevant   relevant information information pertaining
    are missing.   information pertaining   pertaining to the to decision variables
        to the variables and   variables and fail to and constraint. All
        fail to present   present relevant relevant formulas are
        relevant calculations.   calculations. shown with correct
              syntax.
Simulation and result No simulation is Some part of   Most part of the   Correct simulation but Excellent simulation
(40 marks) performed simulation is correct   simulations are   minor error in result. with correct result.
        correct.      
Results interpretation No simulation is Average   Good interpretation   Interpretation of Excellent
(10 marks) performed and interpretation of   of results using   results is well interpretation of
  therefore no results; no use of   relevant data analysis   presented using results using relevant
  interpretation is relevant statistical   but fails to show the   relevant statistical statistical
  provided. terminologies; fail to   implication of result   terminologies but fails terminologies; show
    show the implication   on any application.   to show the the implication of
    of result on any       implication of result result on any
    application.       on any application. applicataion.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


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