Question

A hospital conducted a survey to estimate the mean length of stay at the hospital. a simple random sample of 100 patients resulted in a sample mean of 4.5 days. the population standard deviation is 4 days.

a) Calculate a 90% confidence interval.

b)Interpret the results of your confidence interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 4.5

Population standard deviation =    = 4
Sample size = n =100

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645 ( Using z table )

Margin of error = E = Z_/2    * ( /n)

= 1.645 * (4 /  100 )

= 0.6580
At 90% confidence interval estimate of the population mean
is,

- E < < + E

4.5 -0.6580 <   < 4.5 + 0.6580

3.8420 <   < 5.1580

( 3.8420 , 5.1580 )

At 90% confidence interval estimate of the population mean
is,( 3.8420 , 5.1580 )