For a particular production facility, the total milk yield per goat (for a 10-month lactation period) has averaged 1180 pounds.

For a particular production facility, the total milk yield per goat (for a 10-month lactation period) has averaged 1180 pounds. In an experiment, 14 goats were randomly selected from the facility and, in addition to their regular diet, they were fed a supplement of crude protein, which is thought to affect milk yield. In the experiment, the yields for these 14 goats were: 1209 1358 1380 1098 1241 1325 1008 1217 1487 1217 1269 1348 1139 1122. Suppose that the milk yields are approximately normally distributed and suppose that the population variance is known to be 13500. Perform a test to determine whether the crude protein supplement affects the mean milk yield of goats from this production facility. State symbolically the null and alternative hypotheses. Find the p-value for the test and interpret it.