The Federal Ministry of Labour plans to submit a report to parliament that will support a new employment law which aims to ensure women workers receive fair treatment in the job market. To support its argument in the report, they commission an independent research institution to conduct a study about the job market. In particular, the research institution plans a survey with the objective of determining if women are, on the average, less likely to succeed in job applications than their male counterparts. The institution selects 100 male and 100 female job applicants (i.e., 200 in total) and records the number of successes in job applications for each of the groups. The samples yield success rates for men and women or 76% and 60%, respectively.

a) Does the data provide evidence that women are less likely to succeed in job application than men with similar backgrounds? Carry out the appropriate hypothesis test.

b) Compute a 95% confidence interval for the difference in the proportion of success of male and female job applicants.