1. during fiscal year 2004, the mean monthly benefit per person participating in the federal food-stamp program in nebraska was $79.52. due to the poor economy, more people are using this support program to purchase eligible food. a random sample of 15 people using food stamps was obtained. assume the distribution of monthly benefit per person is normal, the population standard deviation is $4.50. the significance level α is 0.05. a hypothesis test is performed to determine if there is enough evidence to suggest the true mean monthly benefit per person has increased? if the true mean monthly benefit per person is $82, find (a) the probability of committing the type i error. (b) the power of the test. (c) the probability of committing the type ii error.