_ yo Zoalculated _ cr 0; NE Ycritical = Zcritical(df) + H0 1. (10 points) Suppose that a researcher is interested in the amount of air pollution of major cities in North America. Therefore, this researcher recorded the amount of pollution from 100 different metropolitan areas across North America. The sample mean air pollution (measured as the air quality index, or AQI) was Y = 132 and a sample standard deviation was S = 18. a. (3 points) From previous work, it was hypothesized that new emissions policies could reduce the population mean pollution to an AQI of 105. Conduct a hypothesis test at a = 0.05 to determine if these data provide enough evidence to conclude that thf S'hamide 1| '1 mean AQI is less than 105. Show all appropriate work and provme a complete conclusion. b. (5 points) Assuming that a = 0.05 , calculate the probability of a Type 11 error (i.e., ,8) if the actual population mean AQI across all North American cities is 99. As part of this draw the density function under the null hypothesis and then also draw the density function assuming pa is 99. On these density functions, show and LABEL the rejection region and shade in the area that corresponds to the probability of a Type 11 error. c. (2 points) If the researcher conducting this experiment increased the Type I Error rate, would the power increase or decrease? Justify your answer in one or two sentences