Mathematics and Statistics
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)
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)
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x |
1 |
2 |
3 |
4 |
5 |
6 |
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P(x) |
0.14 |
0.26 |
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0.3 |
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0.15 |
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0.08 |
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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
Task 2 (20 marks)
a. 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.
b. Use the relative frequency approach to find the probability distribution for the union membership.
c. Draw the bar chart for the probability distribution of union membership.
d. Define the probability distribution based on part (b), for example (You have to calculate according to your data)
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x |
0 |
1 |
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P(x) |
0.54 |
0.46 |
e. Based on the probability distribution draw the bar chart.
f. 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
i. Find the probability of exactly two
ii. Find the probability less than two
iii. Find the probability at least six
Task 3 (20 marks)
a. 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.
b. Is this a one-tailed or two-tailed test? Briefly explain the reasoning behind your answer.
c. (c) Write, in precise symbolic form, the null and alternative hypotheses.
d. Define Z or T test and also calculate the value of test statistics.
e. Define critical values based on the nature of the problem.
f. State the conclusion based on the sample evidence.
g. Find 99% confidence interval for the Wages (dollar per hours) in the population.
h. 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.
i. Make the decision based on the critical value.
j. Find 95% confidence interval for the Wages (dollar per hours) in the population.
Task 4 (20 marks)
a. 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.
b. Define the mean proportion.
c. 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.
d. Write, in precise symbolic form, the null and alternative hypotheses.
e. Is this a one-tailed or two-tailed test? Briefly explain the reasoning behind your answer.
f. State the conclusion based on the sample evidence.
g. Find 95% confidence interval for the Indicator variable for sex female.
Task 5 (20 marks)
a. 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).
b. State the slope coefficient of the least square regression equation.
c. State the intercept coefficient of the least square regression equation.
d. 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.
e. Estimate the Wages when the work experience is 25 years.
f. 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.
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Marking Criteria |
Not satisfactory |
Satisfactory |
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Good |
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Very Good |
Excellent |
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(0-49%) of the |
(50-64%) of the |
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(65-74%) of the |
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(75-84%) of the |
(85-100%) of the |
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criterion mark) |
criterion mark |
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criterion mark |
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criterion mark |
criterion mark |
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Theoretical |
All the tasks are not |
Some questions are |
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Majority of the |
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Majority of the |
All questions are |
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understanding of |
interpreted, and |
correctly answered |
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questions are |
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questions are |
correctly answered, |
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statistical data |
questions are not |
but most questions |
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correctly answered |
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correctly answered, |
and significance of the |
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analysis (20 marks) |
correctly answered. |
are partially correct. |
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but significance of the |
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and significance of the |
result is well |
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result is not explained |
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result is explained |
explained to show its |
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practical relevance. |
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Problem set-up in |
Fail to set-up problem |
Statistical data |
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Statistical data |
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Statistical data |
Statistical data |
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Excel (30 marks) |
correctly in excel. |
analysis is correctly |
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analysis is correctly |
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analysis is correctly |
analysis is correctly |
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set-up, but all other |
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set-up in excel with |
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set-up in excel with |
set-up in excel with all |
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relevant information |
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most of the of correct |
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majority of correct & |
correct & relevant |
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pertaining to analysis |
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& relevant |
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relevant information |
information pertaining |
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are missing. |
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information pertaining |
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pertaining to the |
to decision variables |
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to the variables and |
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variables and fail to |
and constraint. All |
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fail to present |
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present relevant |
relevant formulas are |
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relevant calculations. |
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calculations. |
shown with correct |
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syntax. |
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Simulation and result |
No simulation is |
Some part of |
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Most part of the |
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Correct simulation but |
Excellent simulation |
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(40 marks) |
performed |
simulation is correct |
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simulations are |
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minor error in result. |
with correct result. |
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correct. |
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Results interpretation |
No simulation is |
Average |
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Good interpretation |
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Interpretation of |
Excellent |
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(10 marks) |
performed and |
interpretation of |
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of results using |
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results is well |
interpretation of |
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therefore no |
results; no use of |
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relevant data analysis |
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presented using |
results using relevant |
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interpretation is |
relevant statistical |
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but fails to show the |
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relevant statistical |
statistical |
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provided. |
terminologies; fail to |
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implication of result |
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terminologies but fails |
terminologies; show |
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show the implication |
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on any application. |
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to show the |
the implication of |
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of result on any |
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implication of result |
result on any |
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application. |
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on any application. |
applicataion. |