Question

According to the Agency for Healthcare Research and Quality, the average cost of a hospital stay is $10,400 per day with a standard deviation of $17,494 per day. A random sample of 7,200 stays in an Idaho hospital had an average cost of $12,30. Determine whether there is evidence that the Idaho hospital has an average cost that is higher than the national average. In the box below, write your conclusion using a significance level of 0.05.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 10400
Alternative Hypothesis, Ha: μ > 10400

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.645.
Hence reject H0 if z > 1.645

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (12300 - 10400)/(17494/sqrt(7200))
z = 9.22

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.