Question

The average length of stay in U.S. hospitals 4.5 days. The length of stay in days of a random sample of patients at a local hospital was recorded.

3,6,3,7,8,9,4,6,5,5,7,3,3,5,8,5

A). Use this data to construct a 99% confidence interval. What are the upper and lower bounds?

B). Based on your confidence interval, is the length of stay at this local hospital significantly different from the national average at the 1% significance level?

Answer 1

The average length of stay in U.S. hospitals 4.5 days. The length of stay in days of a random sample of patients at a local hospital was recorded.

3,6,3,7,8,9,4,6,5,5,7,3,3,5,8,5

A). Use this data to construct a 99% confidence interval. What are the upper and lower bounds?

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	1.9653
Sample Mean	5.4375
Sample Size	16
Confidence Level	99%
Intermediate Calculations
Standard Error of the Mean	0.4913
Degrees of Freedom	15
t Value	2.9467
Interval Half Width	1.4478
Confidence Interval
Interval Lower Limit	3.9897
Interval Upper Limit	6.8853

99% CI = ( 3.9897, 6.8853)

B). Based on your confidence interval, is the length of stay at this local hospital significantly different from the national average at the 1% significance level?

The 99% CI ( 3.9897, 6.8853) contains the value 4.5. Therefore, the length of stay at this local hospital not significantly different from the national average at the 1% significance level.