As a social scientist, you are studying the issue surrounding the declining population growth rate in Singapore. Data relating to the number of registration of marriage was collected.
(a) Construct relevant tables and plot a 10-year(2010 – 2020) time series chart that shows the trend in the number of marriages in Singapore. What can we conclude about the growth rate of marriage in Singapore, especially for the Chinese and the inter-ethnicity marriage? What useful information can be derived from the charts about the marriage trend in the last 10 years, especially in the last 2 years?
(b) Produce a scatter plot with best fit linear trend line. What is the linear regression equation? Describe what you think are the factors underpinning this trend?
Briefly describe three (3) possible social consequences that may happen in 5-10 years lime if this social phenomenon were not addressed.
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In a well-functioning labor market, individuals with the same productive attributes (e.g. education attainment, working experience) should be equally paid. The existence of a public-private “pay gap” for individuals with similar productive characteristics thus has deep implications for efficiency and equity in the labor market.
Use the 5% significance level and the 95% confidence level where relevant.
(a) Describe and compare the distribution of the wage of public and private employees. (Hint: with respect to the Centre of Location, Data Spread and Shape).
(b) Construct a histogram of the wage distribution for the public and private sector employees respectively. Interpret the graphs carefully.
(c) What are the main differences in demographic and social-economic characteristics between employees in the public and private sector? Aid your answer with appropriate tables/graphs, and provide your comments.
(d) Propose and execute a statistical method to estimate the mean hourly wage rate for all public sector employees and all private-sector employees, respectively.
(e) A media report claims that the mean hourly wage rate for all public sector employees was $ 49. Do you agree? Perform a hypothesis test at the 5% significance level. Clearly label your diagram and indicate any assumptions made. Explain carefully if any potential errors in your decision-making.
f. Since the summary data suggests a higher mean hourly wage rate in the public sector, a union lobbyist concludes that the population means hourly wage rates are not equal between the two sectors. Do you agree? Propose and execute a statistical method to examine if the population mean hourly wage rates are equal for the public and private sectors.
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