Question

Two hospital emergency rooms use different procedures for triage of their patients. A local health care provider conducted a study to determine if there is a significant difference in the mean waiting time of patients for both hospitals. The 40 randomly selected subjects from Medina General Hospital (population 1) produce a mean waiting time of 18.3 minutes and a standard deviation of 2.1 minutes. The 50 randomly selected patients from Southwest General Hospital (population 2) produce a mean waiting time of 19.2 minutes and a standard deviation of 2.92 minutes.

Using only the statistical table in your textbook, what is the p-value of the most appropriate hypothesis test?

p > .10

p = .0892

p is between .05 and .10

p is between .025 and .05

p = .0446

p < .025

Answer 1

Let 1waiting time of patient denoted by X which follow Normal distribution.

We take the sample from two different hospitals where

X1~N(18.3,2.1²) ; n1=40

X2~N(19.2,2.92²) ; n2=50

We have to test whether there is a difference between the mean waiting time of patients for both hospitals.

We can write

H0: μ1= μ2

H1: μ1≠ μ2

Define level of significance α=0.05

calculate the test statistic,

Ignore the negative sign, we get the value of test statistic= 1.698

The p-value of the test statistic is P(|Z|>=1.698)= 0.08950776 (From the Z-table).

Hence p-value lies between .05 and .10.