The Wechsler Adult Intelligence Scale (IQ test) is constructed so that Full Scale IQ scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. The mayor of Smart Town believes the county's residents are smarter than the national average and wants to use it (the intelligence of the residents) as a marketing tool to bring industries to the area. A researcher is hired to conduct a study to determine whether Smart County's residents have, on average, higher Full Scale IQs than the population. A random sample of 100 people from Smart County were given the IQ test and were found to have an average Full Scale IQ of 105.

Required:
a. What are the null and alternative hypotheses?
b. What is the value of the test statistic used to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average?