An employee at a water management agency is studying the daily rainfall for last November at region X. The goal is to determine if the region’s mean daily rainfall from last November was below the 4 mm daily average that historically occurs there for the month, at a 5% significance.
a) Write down the null and alternative hypothesis.
b) Rainfall was collected at four randomly chosen locations in region X in five random days last November (a sample size of 20), which resulted in a sample mean of 3.2 smm with a standard deviation of 1 mm. It is well known that the distribution of daily rainfall for November in region X is right asymmetric and highly skewed. Can the employee use a t-test to conduct hypothesis testing here? Why or why not?