Question

A large company wants to estimate the average amount of money that is owed to it by delinquent customers, µ. The mean of this sample is $230 and the standard deviation is $50. Construct a 95% and 99% confidence interval for the population parameter µ.

Only information givin. No sample size. Show by hand step by step.

Answer 1

sample is must for calculating confidence interval

if sample size is not given , then taking $50 as std dev of sampling distribution

for 95% confidence interval,

Level of Significance ,    α =    0.05
Sample Mean,    x̅ =   230
degree of freedom=   DF=n-1=   99
't value='   tα/2=   1.9842
      
Standard Error , SE =   50
margin of error ,   E=t*SE =   99.2108
confidence interval is       
Interval Lower Limit=   x̅ - E =    130.7892
Interval Upper Limit=   x̅ + E =    329.2108

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99% confidence interval,

Level of Significance ,    α =    0.01

't value='   tα/2=   2.6264

margin of error ,   E=t*SE =   131.3203
confidence interval is       
Interval Lower Limit=   x̅ - E =    98.6797
Interval Upper Limit=   x̅ + E =    361.3203