1. A political pollster knows that the average age of Democrat voters in the general population is 39.1. He decides to conduct a further poll (experiment) of 500 voters to see if the average age of Democrat voters in urban areas is different than that in the general population. Assume the standard deviation of Democrat voters in urban areas is 10 years.

a) What are the null and alternative hypotheses for this experiment?

b) Describe, in words, a Type I error for this experiment.

c) Describe, in words, a Type II error for this experiment.

d) What random variable (test statistic) does the pollster need to consider to test this hypothesis? What is its probability distribution? (exact or approximate; explain.)

e) Assume that the null hypothesis is rejected if the sample mean falls outside the region [38.1, 40.1]. What is the probability of a type I error?