value of the test statistic
Past records suggest that the mean annual income,M1 , of teachers in state of Pennsylvania is less than or equal to the mean annual income,M2 , of teachers in Illinois. In a current study, a random sample of 25 teachers from Pennsylvania and an independent random sample of 25 teachers from Illinois have been asked to report their mean annual income. The population standard deviation for mean annual income of teachers in Pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.05 level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of Pennsylvania is less than or equal to the mean annual income of teachers in Illinois? Perform a one-tailed test.
I am trying to fgure out the value of the test statistic I know the mean for X1 = 46896.64 and X2=45334.32. I know that the standard deviation is 6400 and 6100 and that N1 and N2 is 25. My formula is
z=(46896.64-45334.32)-0 divided by the suare root of (6400)2/15 plus (6100)2/15 but I keep coming up with the wrong answer can you please help me