The mean percent of childhood asthma prevalence in 43 cities is 2.28​%. A random sample of 34 of these cities is selected.

Question

What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.6​%? Interpret this probability. Assume that sigma =1.28​% What is the probabitly

Answer 1

The test statistic is (2.6-2.28)/1.28=0.25 corresponding to a probability 0.5987, meaning that 59.87% of the population probably has a mean asthmatic population of less than 2.6%. So 100-59.87=40.13% of asthmatics are more than 2.6% of the overall population. The sample size of 34 is about 79% of the 43 cities constituting the whole population. Since the sample size is so high compared to the population, no adjustment has been made to the standard deviation. I’ve just used the Z score to look up the probability in the Normal Dustribution Table.