Question

A pharmacist has recently started a new private pharmacy and wanted to estimate the average waiting time to get prescribed medication in his pharmacy. He randomly selected 40 patients for observation and recorded how many minutes each waits. The mean waiting time was 28 minutes. Assuming that the waiting time follow a normal distribution with the standard deviation of 4 minutes, estimate the mean waiting time among all patients using a 95% confidence interval. Interpret this interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 28

sample standard deviation = s = 4

sample size = n = 40

Degrees of freedom = df = n - 1 = 40 - 1 = 39

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,39 = 2.023

Margin of error = E = t/2,df * (s /n)

= 2.023 * (4 / 40)

Margin of error = E = 1.28

The 95% confidence interval estimate of the population mean is,

- E < < + E

28 - 1.28 < < 28 + 1.28

26.72 < < 29.28

(26.72 , 29.28)