A philanthropic organization helped a town in Africa dig several wells to gain access to clean water. Before the wells were in place, an average of 120 infants contracted typhoid each month. After the wells were installed, the philanthropic organization surveyed for nine months and found an average of 90 infants contracted typhoid per month. Assume that the population standard deviation is 40 and the number of infants that contract typhoid is normally distributed.

a. Specify the null and alternative hypotheses to determine whether the average number of infants that contract typhoid has decreased since the wells were put in place.

b. Calculate the value of the test statistic and the p-value.

c. At the 5% significance level, can you conclude that the number of babies falling ill due to typhoid has decreased? Explain.