. The personnel department of a large corporation wants toestimate the family de

Question

. The personnel department of a large corporation wants toestimate the family dental
     expenses of its employees to determine thefeasibility of providing a dental insurance
     plan. A random sample of 10employees reveals the following family dental expenses
     (in $) for the preceding year. Assume the distribution is roughly normal with minimal
     outliers. The standard deviation forthe sample below is $138.80.

     110, 362, 246, 85, 510, 208, 173, 425,316, 179

     a. What is the 90%confidence interval estimate of the mean family dental expenses   
           forall employees?

     b. What is the margin oferror in part a.

     c. If you increased yoursample size to 20, how would your margin of error change?

Explanation / Answer

a. What is the 90% confidence interval estimate ofthe mean family dental expenses    
           forall employees?

Given n=10,xbar= 261.4, s=138.8 (based on thedata)

=0.1, t(0.05,df=n-1=9)=1.83 (checkstudent t table)

The 90% CI is

xbar±Z*s/n

-->261.4±1.83*138.8/sqrt(10)

-->( 181.08, 341.72)

     b. What is the margin oferror in part a.

s/n =138.8/sqrt(10) = 43.89

     c. If you increased yoursample size to 20, how would your margin of error change?

s/n =138.8/sqrt(20) = 31.03662

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