Problem 12. A researcher is studying migration patterns. She collected the location of the cur- rent and previous homes for subjects who moved across regions. She recorded the following: Previous home Current home Northeast Southeast West Northeast - 267 255 Southeast 135 - 139 West 240 234 - Here the diagonals are not included since she only studied subjects who moved be- tween regions. She would like to know if the probability of moving from region a to b is the same as the probability of moving from region b to a for all regions a and b. a. Mathematically state her null and alternative hypotheses dening any notation you use. b. Calculate the expected counts under the null hypothesis. c. Perform the Chi-squared test and state your conclusions in the language of the problem. (Hint the df is 3.)