A study of 203 police officers in an eastern state found that their mean salary was $75,500 with a sample standard deviation of $3,000. The same study of 245 police officers in a northern state found that their mean salary was $74,500 with a sample standard deviation of $4,000. Let group 1 be the eastern state police officers and group 2 be the northern state police officers. Find the lower bound of a 95% confidence interval for the mean salary difference of police officers between an eastern state and a northern state. Let us assume that the standard deviations for both groups are the same.