Question

In: Statistics and Probability

Chapter 8. A sample of 36 patients in a doctor's office showed that they had to...

Chapter 8. A sample of 36 patients in a doctor's office showed that they had to wait an average of 45 minutes with a standard deviation of 12 minutes before they could see the doctor.

Please provide a 95% confidence interval estimate for the average waiting time of all the patients who visit this doctor, and interpret your results (write a sentence explaining the results).

Expert Solution

Solution :

Given that,

Point estimate = sample mean = =45

Population standard deviation = = 12

Sample size n =36

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z/2 * ( / $\sqrt$ n)

= 1.96 * ( 12 / $\sqrt$ 36 $\sqrt$ )

E= 3.92
At 95% confidence interval estimate of the population mean
is,

- E < < + E

45 - 3.92 < < 45+ 3.92

41.08 < < 48.92

( 41.08 ,48.92 )

orchestra answered 1 year ago

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