If alpha = .05, calculate the probability of a Type II error (i.e., ) 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 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 II error.

Background information: 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 132 and a sample standard deviation was s = 18. From previous work, it was hypothesized that new emissions policies could reduce the population mean pollution to an AQI of 105.