A labor union representing public sector employees is claiming that the recent government 2- day a week in-person presence in office directive is not in line with current practices in the private sector. They have commissioned a national survey to compare teleworking policies between similar public and private sector employers. The survey looked at two independent random samples of employers: 110 and 140 in the public and private sectors respectively. They found that 73 public sector employers impose a 2-day per week presence in office compared to 75 for private sector employers.

a) [12 marks] Test whether employers in these two sectors are equally likely to impose a 2- day per week presence in office. Use the critical value and p-value approach and a 5% level of significance. Make sure to include all the steps of hypotheses (hypotheses, decision zone, critical value and p-value, conclusion with justification). Show your manual calculations and provide a StatCrunch output confirming your results. [Hint: let p1 be the proportion of the public sector and p2 the proportion of private sector employers who impose a 2-day per week presence in office]. (Manual calculations and StatCrunch)

b) [8 marks] Calculate and interpret an appropriate 95% confidence interval for the true difference between the proportions of public sector and private sector employers who impose a 2-day per week presence in office. Show your Excel or StatCrunch output for verification. (Manual calculations and StatCrunch)

c) [2 marks] Explain how your conclusions in parts a) and b) above are consistent.