Question

According to the Agency for Healthcare Research and Quality, the average length of a hospital stay is 4.5 days. Hospitals can reap many benefits by decreasing the length of patient stays in the hospital. A random sample of 7,200 stays in an Idaho hospital had an average stay of 4.2 days with a standard deviation of 8.3 days. Determine whether there is evidence that the Idaho hospital has an average stay that is lower than the national average. Determine the test statistic and the p-value. Test statistic: Round your answer to two decimal places. P = Use the table. Round your answer to four decimal places.

Answer 1

Solution :

This is the left  tailed test .

The null and alternative hypothesis is ,

H0 :   = 4.5

Ha : < 4.5

Test statistic = z

= ( - ) / / n

= (4.2 - 4.5) / 8.3 / 7200 = -3.07

Test statistic = -3.07

P(z < -3.07) = 0.0011

P-value = 0.0011