For a sample of 40 firms in the Kaiser health coverage survey, the mean monthly cost of the premium for an HMO plan was $405.02. The sample standard deviation of premium costs was $112.08. Assume that the population has a normal distribution. Using a 90% confidence level, find the margin of error.

Answer: 29.7188Step-by-step explanation:As we consider the given description, we haven= 40s= 112.08Since population standard deviation is unknown , so we use t-test.Using t-value table , the critical t- value will be:-[tex]t_{n-1,\ \alpha/2}=t_{39,\ 0.05}=1.677[/tex]The formula to find the margin of error :[tex]E=t_{n-1,\ \alpha/2}\dfrac{s}{\sqrt{n}}[/tex][tex]E=(1.677)\dfrac{112.08}{\sqrt{40}}\\\\=(1.677)(17.7214040076)\\\\=29.7187945207\\\\\approx29.7188[/tex]Hence, the margin of error =29.7188