Question

the moore's discount store chain issues its own credit card. the credit manager wants to find out whether the mean monthly unpaid balance is 430$. the credit manager decides to take a random sample of 5 unpaid card balances. they are as follows: 375$, 452$, 394$, 422$, 392$. assume original population of unpaid card balance is normal. compute 95% confidence interval for the true mean monthly unpaid credit balance.

Answer 1

	Values ( X )	Σ ( Xi- X̅ )2
	375	1024
	452	2025
	394	169
	422	225
	392	225
Total	2035	3668

Mean X̅ = Σ Xi / n
X̅ = 2035 / 5 = 407
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 3668 / 5 -1 ) = 30.282

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 5- 1 ) = 2.776
407 ± t(0.05/2, 5 -1) * 30.282/√(5)
Lower Limit = 407 - t(0.05/2, 5 -1) 30.282/√(5)
Lower Limit = 369.406
Upper Limit = 407 + t(0.05/2, 5 -1) 30.282/√(5)
Upper Limit = 444.594
95% Confidence interval is ( 369.406 , 444.594 )