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)

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

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)

x

0

1

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.

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.