# V2 = Occupational category (1=Management, 2=Sales, 3=Clerical, 4=Service, 5=Professional,

01 / 10 / 2021 Statistics

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SBM3103, Mathematics and Statistics
The dataset included with this assignment is a random sample of 534 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 60 IDs each containing observations, where appropriate, of the eight variables V1 to V8. The variables in the data set are as follows:
V1 = Wage (dollars per hour)
V2 = Occupational category (1=Management, 2=Sales, 3=Clerical, 4=Service, 5=Professional,
6=Other)
V3 = Sector (0=Other, 1=Manufacturing, 2=Construction)
V4 = Indicator variable for union membership (1=Union member, 0=Not union member)
V5 = Number of years of education
V6 = Number of years of work experience
V7 =Age (years)
V8 = Indicator variable for sex (1=Female, 0=Male).
Answers to the assignment 2 tasks must be based on the sample data file that you created in Part I of the assignment. Most tasks in the assignment 2 require you to obtain an Excel output prior to performing some analysis. There are five tasks in the assignment 2.  You must meet all task requirements to receive full 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 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
(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
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
(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 po

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