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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
Task 5 (10 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 from task 1)
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 6 (10 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) 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 7 (10 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 8 (10 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 excel 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
frame from task 1)
(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.
