Confidence Interval Mean A random sample of 48 days taken a

Confidence Interval – Mean

A random sample of 48 days taken at a large hospital shows that an average of 38 patients were treated in the emergency room per day. The standard deviation of the population is 4. Find the 99% confidence interval of the mean number of ER patients treated each day at the hospital.

Find the critical value:

Find the margin of error:E =

Find the confidence interval: CI =

Write the conclusion.

Solution

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=38
Standard deviation( sd )=4
Sample Size(n)=48
Confidence Interval = [ 38 ± Z a/2 ( 4/ Sqrt ( 48) ) ]
= [ 38 - 2.58 * (0.5774) , 38 + 2.58 * (0.5774) ]
= [ 36.5104,39.4896 ]

We are 95% confident that mean number of ER patients treated each day at the hospital is between the above range