Question 1. [7 marks total] Parental leave is often compensated to some degree, but the amount of compensation varies greatly. You read a research article that stated, "across people of all incomes, 47% of leave-takers received full pay during their leave, 16% received partial pay, and 37% received no pay." After reading this, you wonder what the distribution of parental leave payment pay is for low income households. Suppose you conduct a survey of leave-takers within households earning less than $30,000 per year. You surveyed 225 people (selected in a random sample) and found that 51 received full pay, 33 received partial pay, and 141 received no pay..You would like to investigate whether the distribution of pay for households earning < $30,000 is different from that of all income levels. Does this correspond to a chi-square test of independence or a chi-square test for goodness of fit?

Goodness of fit Chi-squared test gives confirmation on whether a separately observed frequency distribution differs from a theoretical or general distribution.

In this case, the researcher studies a fraction of income earners - low income earners. He is interested in knowing whether the distribution of pay of low income earners is different from the distribution of pay of ALL income earners.

This survey hence corresponds to a chi-square test for goodness of fit.