Apply confidence intervals and hypothesis testing methods to

Apply confidence intervals and hypothesis testing methods to form conclusions about the population. A hospital has two walk in clinics. The hospital was interested in whether the average waiting time for patients was different between the two clinics. A random sample of patients from each clinic is taken and waiting times are recorded. Sample data is as follows. (Data is in minutes.) Conduct a hypothesis test to determine if there is a significant difference in the population means Be sure to verify that the problem meets the requirements for performing the test before you start. You must show all steps and state your conclusion clearly. Use alpha = 0.05 level of significance

Solution

H0: mu1 = mu2

Ha: mu1 not equal to mu2

Two tailed test.

z for 95% CI= 1.96
declare p larger than alpha=0.05 not significant.

mean1 eq: 18.5 (variance= 13.69) (se= 0.6002)
mean2 eq: 20.1 (variance= 1.96) (se= 0.1941)

Difference between means:
M1-M2=18.5-20.1=-1.6
sd=4.222; se=0.6308

95% CI of difference:
-2.8364 <-1.6< -0.3636

t-difference: -2.536
df-t: 44.3; p= 0.0156

As p <0.05, reject null hypothesis.

There is sign. difference in the two clinics.