During the winter months, air quality can be bad because of weather inversions. Stations around the state of Utah monitor particulate matter in the air and generate an Air Quality Index, AQI. An AQI above 50 can be unhealthy. For winter months in 2019, a random sample of 35 days in Salt Lake City found that the average AQI was 38 with a standard deviation of 27. Find and interpret a 95% confidence interval for the average AQI during these months.

Include:Requirement check

• Correct test type (one sample z, one-sample t, one proportion z, two proportion z)
• Null and alternative hypotheses
• Test statistic and p-value
• Conclusion in the context of the problem