Question

The postanasthesia care area (recovery room) at St. Luke’s hospital was recently enlarged. The hope was that with the enlargement the mean number of patients per day would be more than 25. A random sample of 15 days revealed the following numbers of patients: 25 27 25 26 25 28 28 27 24 26 25 29 25 27 24 Can we conclude that the number of patients is now higher than 25? Use a 0.05 significance level. (Be sure your answer is in the appropriate format.)

Answer 1

We have to test the claim that the the mean number of patients per day would be more than 25.

Null and alternative hypothesis are

Here population standard deviation is unknown and sample size is small, we use t test statistic for one population mean.

df = n - 1=15-1=14

One tail area = Level of significance = 0.01

Look in t table for df = 14 and One tail area = Level of significance = 0.05 and find t critical value.

The t-critical value for a right-tailed test, for a significance level of α=0.05 is

t_c = 1.761

Reject H0 , if t test statistic value > t critical value, otherwise we fail to reject H0.

Since t test statistic value = 2.694 >t critical value = 1761 , we reject H0 .

Since we have rejected H0, we conclude that there is sufficient  evidence to conclude that: the the mean number of patients per day is more than 25.

Hope this will be helpful. Thanks and God Bless You :)