The mean salary of actuaries is LaTeX: \mu=\$100,000=$100,000 and the standard deviation is LaTeX: \sigma=\$36,730=$36,730. You are interested to know if the mean salary for women actuaries is different from the population mean, but are not sure if it is higher or lower. You set up a hypothesis test with level of significance LaTeX: \alpha=0.05=0.05 and LaTeX: H_0:~~\mu=100,000H0: =100,000 LaTeX:H_a:~~\mu\neq100,000H: ≠100,000 You collect a simple random sample of LaTeX: n=36=36 women's salaries and find that LaTeX: \bar{x}=\$111,000x¯=$111,000. Use this information for next three questions. What is the lower limit of this 95% confidence interval? (Round to the nearest whole number)