a random sample of 45 days taken at a large hospital shows that a mean of 37 patients were treated in the emergency room (ER) per day. The standard deviation of the population is 4. Find the 95% confidence interval of the mean number of ER patients treated each day at the hospital. Express your answers as decimals to the nearest hundredth , please show work and formulas used to solve this , thanks so much!
Solution :
Given that,
Point estimate = sample mean = = 37
Population standard deviation = = 4
Sample size = n = 45
At 95% confidence level the z is ,
Z/2 = Z0.025 = 1.96
Margin of error = E = Z/2* ( /n)
= 1.96* ( 4/ 45)
= 1.17
At 95% confidence interval estimate of the population mean is,
- E < < + E
37 - 1.17 < < 37 + 1.17
35.83 < < 36.17
( 35.83 , 36.17 )
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