Georgianna claims that in a small city renowned for its music school, the average child takes less than 5 years of piano lessons. We have a random sample of 20 children from the city, with a mean of 4.6 years of piano lessons and a standard deviation of 2.2 years. 

(a) Evaluate Georgianna's claim (or that the opposite might be true) using a hypothesis test. 

(b) Construct a 95% confidence interval for the number of years students in this city take piano lessons, and interpret it in context of the data. 

(c) Do your results from the hypothesis test and the confidence interval agree? Explain your reasoning.