Question

Your hospital is negotiating with medical insurance providers, who would like to reduce the amount they pay as reimbursement for hospital stays. For a particular procedure, they would like to reduce payment by $300 and have patients go home one day earlier. To see what effect this would have on hospital costs, a random sample of 50 patients who were recently admitted for this procedure was analyzed. Had they left one day earlier, the average savings would have been $322.44, and the standard deviation was found to be $21.71. Construct a 95% confidence interval for the mean savings, per patient, for the larger population of recent patients.

(1) specify the business and statistical hypotheses
(2) specify what the Type I and Type II errors are in this business context, and, the implications of making those errors
(3) include the results from Minitab, (4) draw appropriate conclusions to your statistical hypotheses based on the results
(5) present the business conclusions in a short non-statistical summary.

Answer 1

(1) specify the business and statistical hypotheses

Null hypothesis	H₀: μ = 300
Alternative hypothesis	H₁: μ < 300

(2) specify what the Type I and Type II errors are in this business context, and, the implications of making those errors

Type I error: Conclude that μ < 300 when μ = 300.

Type II error: Fail to reject that μ = 300 when μ < 300.

(3) include the results from Minitab,

(4) draw appropriate conclusions to your statistical hypotheses based on the results

Since the p-value (1.000) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that μ < 300.

(5) present the business conclusions in a short non-statistical summary.

Reducing the amount they pay as reimbursement for hospital stays is necessary.