Question

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 1

Answer: 29.7188

Explanation:

As we consider the given description, we have

n= 40

s= 112.08

Since population standard deviation is unknown , so we use t-test.

Using t-value table , the critical t- value will be:-

`t_(n-1,\ \alpha/2)=t_(39,\ 0.05)=1.677`

The formula to find the margin of error :

`E=t_(n-1,\ \alpha/2)(s)/(√(n))`

`E=(1.677)(112.08)/(√(40))\\\\=(1.677)(17.7214040076)\\\\=29.7187945207\\\\\approx29.7188`

Hence, the margin of error =29.7188