Statistics: Confidence Intervals and Sample Size

STATISTICS
[Document subtitle]
[DATE]

Sample mean = $600
Sample standard deviation = $500
Number of samples = 400
(1) 95% confidence interval for the mean of all the claims processed by the insurance
company next year
The t value for 95% confidence interval = 1.9659
Standard error = Sample standard deviation/ sqrt (Number of samples) = 500/ sqrt (400) = 25
Margin of error = t value * Standard error = 1.9659*25 = 49.147
Lower limit of 95% confidence interval = Mean - Margin of error = 600 – 49.147 =550.85
Upper limit of 95% confidence interval = Mean +Margin of error= 600 +49.147 =649.15
95% confidence interval = [ 550.85 649.15]
It can be said with 95% confidence that mean of all the claims processed by the insurance
company next year would fall between 550.85 to 649.15.
(2) Percentage of the claims processed by the insurance company next year that would
exceed $1000 and also 95% confidence interval for this percentage
Percentage of the claims processed by the insurance company next year that would exceed
$1000 = (50+20+10)/(250+70+50+20+10) = 0.20 or 20%
95% confidence interval for this percentage is computed below.
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