Calculate a 95% confidence interval for the standard deviation of Total Cost for all customers (assuming...
Calculate a 95% confidence interval for the standard deviation of Total Cost for all customers (assuming that Total Cost follows normal distribution).
n 400
Variance $9,481.51
Std Dev 97.37
Sample mean $153.82
Homework Answers
Solution :
Given that,
= $153.82
s = $97.37
n = 400
Degrees of freedom = df = n - 1 = 400 - 1 = 399
At 95% confidence level the t is,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
t /2,df =
t0.025,399 = 1.966
Margin of error = E =
t/2,df * (s /
n)
= 1.966* (97.37 /
400)
= 9.571
The 95% confidence interval estimate of the population mean is,
- E < 
< + E
153.82 - 9.571 <
< 153.82 + 9.571
144.249 < < 163.391
(144.249, 163.391)
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