Question

Sulfur dioxide affects human health when it is breathed in by irritating the nose, throat, and airways to cause coughing, wheezing, shortness of breath, or a tight feeling around the chest. The effects of sulfur dioxide are felt very quickly and most people would feel the worst symptoms in 10 or 15 minutes after breathing it in. Those most at risk of developing problems if they are exposed to sulfur dioxide are people with asthma or similar conditions (Australian Government, Sulfur dioxide (SO2) c). The United States Environmental Protection Agency has set a standard that sulfur dioxide (SO2) should not exceed 75 parts per billion (PPB) over a one-hour period. Fortunately, the United States has done a good job at reducing sulfur dioxide in the atmosphere. To determine if the average SO2 of cities in the United States is less than 75 ppb, a random sample of 41 cities in the United States was taken. The average SO2 levels of the 41 cities was = 30.5 ppb. (Note: the data used in this example is a bit old. SO2 levels have actually decreased more since these data were collected!) The histogram below is of an adjusted bootstrap distribution (i.e., bootstrap distribution created if the null hypothesis is true) based on 10,000 adjusted bootstrap sample means. Adjusted Bootstrap Distribution of Sample Means 1500 Frequency 0 500 65 70 75 80 85 90 adjusted bootstrap sample means (ppb) Based on this histogram, the p-value is approximately – 0 <0.0001 0.05 0.1 0.5 1

Answer 1

From the given information the approximate standard deviation is, (Upper value - Lower value) ()= Standard deviation (o 4 Let, Upper value from the graph be 87 and lower value is 67. (Upper value -Lower value) Standard deviation (o) 4 87 – 67 %3D 4 = 5 The Z score of the given test is, o Nn 30.5 – 75 5/ /41 =-56.988 P = NORMSDIST (-56.988) [Excel function] 0.0000 <0.0001 Correct option: < 0.0001