A major bank implemented a number of policies and procedures to try to ensure that its female employees have as much opportunity for advancement as its male employees. The bank decided to check employees' perceptions of opportunity for advancement. A random sample of 240 female employees indicated that 82.5% felt that female employees had as much opportunity for advancement as male employees.
A random sample of 350 male employees indicated that 94.3% of male employees thought that female employees had as much opportunity for advancement as male employees. Is there evidence, at a 5% significance level, that the proportion of female employees is more than 10% lower than the proportion of male employees? The total number of employees at the bank is over 65,000.