Short Message Service (SMS) is the formal name for the communication service that allows the interchange of short text messages between mobile telephone devices. About 75% of mobile phone subscribers worldwide send or receive SMS text messages. Consequently, SMS provides a opportunity for direct marketing. In Management Dynamics (2007), marketing researchers investigated the perceptions of college students towards SMS marketing. For one portion of the study, the researchers applied the Wilcoxon rank sum test to compare the distributions of the number of text mes sages sent and received during peak time for two groups of cell phone users: those on an annual contract and those with a pay-as-you-go option.

a. Specify the null hypothesis tested in the words of the problem.

b. Give the formula for the large-sample test statistic if there were 25 contract users and 40 pay-as-you-go users in the sample.

c. The Wilcoxon test results led the researchers to conclude "that contract users sent and received significantly more SMS's during peak time than pay-as-you-go users." Based on this information, draw a graph that is representative of the two SMS usage rate populations.