Insurance is an import ant part of family spending Average car insurance per car

Question

Insurance is an import ant part of family spending Average car insurance per car is of interest to investigate. A random sample of 25 families are surveyed and we obtain the average car insurance premium is $780 and S.d. is $ 120 per year. Assume the car insurance premium is normally distributed. Find a 99% confidence interval for the average car insurance premium and interpret your result. What is the margin of error when using $780 to estimate the population average car insurance premium with 99% confidence?

Explanation / Answer

a.
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=780
Standard deviation( sd )=120
Sample Size(n)=25
Confidence Interval = [ 780 ± t a/2 ( 120/ Sqrt ( 25) ) ]
= [ 780 - 2.797 * (24) , 780 + 2.797 * (24) ]
= [ 712.87,847.13 ]
  
b.
Margin Of Error = Upper - Lower /2 = (847.13 - 712.87)/2 = 67.13

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