Question

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!

Answer #1

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}
= Z_{0.025} = 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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