Question

The daily net cash flows in the table below represent a 5-day sample. Use the Data Analysis tool in Excel to calculate the 95% and 99% confidence intervals for the daily net cash flows. Along with your calculation, interpret the meaning behind your confidence interval estimates and discuss why the 99% confidence interval is wider.

Day	Net Cash Flow
1	15,000
2	17,000
3	13,000
4	20,000
5	14,000

Answer 1

Solution:

Here, we have to find the 95% and 99% confidence intervals for the daily net cash flow by using the excel.

The excel output for the 95% confidence interval for the average daily net cash flow is given as below:

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	2774.887385
Sample Mean	15,800
Sample Size	5
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	1240.967365
Degrees of Freedom	4
t Value	2.7764
Interval Half Width	3445.4778
Confidence Interval
Interval Lower Limit	12354.52
Interval Upper Limit	19245.48

The excel output for the 99% confidence interval for the average daily net cash flow is given as below:

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	2774.887385
Sample Mean	15,800
Sample Size	5
Confidence Level	99%
Intermediate Calculations
Standard Error of the Mean	1240.967365
Degrees of Freedom	4
t Value	4.6041
Interval Half Width	5713.5315
Confidence Interval
Interval Lower Limit	10086.47
Interval Upper Limit	21513.53

From above two intervals, it is observed that the 99% confidence interval is wider than the 95% confidence interval. We are given that all other values are same for both intervals. The margin of error is more for 99% interval, and this is due to t critical value. The t critical value for 99% confidence interval is more than the t critical value for 95% interval. In 99% confidence interval, we are more confident about the interval for the population mean and that’s why the 99% confidence interval is wider.