Biostatistics question

Question

2. The US Census bureau is interested in capturing vital statistics that may or may not be directly related to health outcomes. One such statistic is annual income. Assume that the Census bureau conducts a SRS of 758 and determines that the average sample income is $72,487.00.

A) Assume the bureau uses a σ=$1,254.00. Find out a confidence interval (95%) for the average annual income variable.


B) Interpret the interval calculated in the above response.

Answer 1

Since we already know a lot about the information necessary to solve this problem (and that a two-sided 95% confidence interval has a z-score = 1.96), let's go ahead and fill in the formula for a confidence interval:

 

[X-bar - Z *(std. error) , X-bar + Z *(std. error)]=

 

[72,487 - (1.96)*(1,254/758),72,487 + (1.96)*(1,254/758)] =

 

( Lower limit, Upper limit)

 

You should be able to solve the equation from here by following the simple order-of-operations technique from algebra.