Question

In: Statistics and Probability

The postanesthesia care area (recovery room) at St. Luke’s Hospital in Maumee, Ohio, was recently enlarged....

The postanesthesia care area (recovery room) at St. Luke’s Hospital in Maumee, Ohio, was recently enlarged. The hope was that the change would increase the mean number of patients served per day to 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

At the 0.01 significance level, can we conclude that the mean number of patients per day is more than 25?

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  1. What is the decision rule? (Round your answer to 3 decimal places.)
  1. Compute the value of the test statistic. (Round your answer to 3 decimal places.)
  1. What is your decision regarding H0?
  1. Estimate the p-value.

Solutions

Expert Solution

a. Here claim is that mean is more than 25

vs

Reject the null hypothesis if test-statistic > 2.62

Now sample mean is

Create the following table.

data data-mean (data - mean)2
25 -1.0667 1.13784889
27 0.9333 0.87104889
25 -1.0667 1.13784889
26 -0.066700000000001 0.0044488900000001
25 -1.0667 1.13784889
28 1.9333 3.73764889
28 1.9333 3.73764889
27 0.9333 0.87104889
24 -2.0667 4.27124889
26 -0.066700000000001 0.0044488900000001
25 -1.0667 1.13784889
29 2.9333 8.60424889
25 -1.0667 1.13784889
27 0.9333 0.87104889
24 -2.0667 4.27124889

Standard deviation is

b. So test statistics is

c. As test statistics is greater than 2.62, we reject the null hypothesis

d. P value is TDIST(2.694,14,1)=0.0087


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